I agree with Ciencia. It seems to be a problem with the new session handling in 1.27. In 1.26.x I've never lost my sessions. It seems so, that my sessionID changes every time when I send a request to the server (I don't switch between http and https). But I don't have a reason and not a solution. So I post the error.log here.
Start request POST /wiki/index.php?title=Spezial:Anmelden&returnto=Hauptseite
HTTP HEADERS:
HOST: MyServer.de
USER-AGENT: Mozilla/5.0 (Windows NT 6.1; WOW64; rv:47.0) Gecko/20100101 Firefox/47.0
ACCEPT: text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8
ACCEPT-LANGUAGE: de,en-US;q=0.7,en;q=0.3
ACCEPT-ENCODING: gzip, deflate
DNT: 1
REFERER: http://MyServer.de/wiki/index.php?title=Spezial:Anmelden&returnto=Hauptseite
COOKIE: __utma=160677477.911326897.1398857347.1467369865.1467636887.185; __utmz=160677477.1422875023.52.3.utmcsr=google|utmccn=(organic)|utmcmd=organic|utmctr=(not%20provided); my_wikiUserName=MyUserName; __utmc=160677477; MyGitWikiSession=ge9bns6c6h48et2s4rrjs3v45h9psflf; my_wikilanguage=en; uls-previous-language-autonym=English; mw_installer_session=sh49d0t4af333d2jrb39n8ni37; IPBWikiSession=nifd5814p6ns4l022hnlllm4v0; ipb_wikiUserID=1; ipb_wikiUserName=MyUserName; ipb_wikiToken=f3eb3f4043d61703fec60a996fb7d0b0
CONNECTION: keep-alive
PRAGMA: no-cache
CACHE-CONTROL: no-cache
CONTENT-TYPE: application/x-www-form-urlencoded
CONTENT-LENGTH: 185
[caches] cluster: APCBagOStuff, WAN: mediawiki-main-default, stash: db-replicated, message: APCBagOStuff, parser: APCBagOStuff
[caches] LocalisationCache: using store LCStoreCDB
[session] Session "ge9bns6c6h48et2s4rrjs3v45h9psflf" requested without UserID cookie
[session] SessionBackend "ge9bns6c6h48et2s4rrjs3v45h9psflf" is unsaved, marking dirty in constructor
MWCryptRand::realGenerate: Generating cryptographic random bytes for MediaWiki\Session\SessionManager->generateSessionId/MWCryptRand::generateHex/MWCryptRand->realGenerateHex/MWCryptRand::generate/MWCryptRand->realGenerate
MWCryptRand::realGenerate: openssl_random_pseudo_bytes generated 20 bytes of strong randomness.
MWCryptRand::realGenerate: 0 bytes of randomness leftover in the buffer.
[session] SessionBackend "n94eau9g0hoeo1397jtdsf281grae587" metadata dirty due to ID reset (formerly "ge9bns6c6h48et2s4rrjs3v45h9psflf")
[session] SessionBackend "n94eau9g0hoeo1397jtdsf281grae587" save: dataDirty=1 metaDirty=1 forcePersist=0
[cookie] setcookie: "MyGitWikiSession", "n94eau9g0hoeo1397jtdsf281grae587", "0", "/", "", "", "1"
[cookie] already deleted setcookie: "my_wikiUserID", "", "1436186784", "/", "", "", "1"
[cookie] already deleted setcookie: "my_wikiToken", "", "1436186784", "/", "", "", "1"
[cookie] already deleted setcookie: "forceHTTPS", "", "1436186784", "/", "", "", "1"
[session] SessionBackend "n94eau9g0hoeo1397jtdsf281grae587" save: dataDirty=1 metaDirty=1 forcePersist=0
[cookie] already set setcookie: "MyGitWikiSession", "n94eau9g0hoeo1397jtdsf281grae587", "0", "/", "", "", "1"
[cookie] already deleted setcookie: "my_wikiUserID", "", "1436186784", "/", "", "", "1"
[cookie] already deleted setcookie: "my_wikiToken", "", "1436186784", "/", "", "", "1"
[cookie] already deleted setcookie: "forceHTTPS", "", "1436186784", "/", "", "", "1"
[cookie] already set setcookie: "MyGitWikiSession", "n94eau9g0hoeo1397jtdsf281grae587", "0", "/", "", "", "1"
[cookie] already deleted setcookie: "my_wikiUserID", "", "1436186784", "/", "", "", "1"
[cookie] already deleted setcookie: "my_wikiToken", "", "1436186784", "/", "", "", "1"
[cookie] already deleted setcookie: "forceHTTPS", "", "1436186784", "/", "", "", "1"
IP: 192.124.243.164
[session] SessionBackend "n94eau9g0hoeo1397jtdsf281grae587" Taking over PHP session
Fully initialised
[MessageCache] MessageCache::load: Loading de... local cache is empty, got from global cache
[MessageCache] MessageCache::load: Loading en... local cache is empty, got from global cache
Unstubbing $wgParser on call of $wgParser::firstCallInit from MessageCache->getParser
Parser: using preprocessor: Preprocessor_DOM
Unstubbing $wgLang on call of $wgLang::_unstub from ParserOptions->__construct
QuickTemplate::__construct was called with no Config instance passed to it
MWCryptRand::realGenerate: Generating cryptographic random bytes for PasswordFactory::generateRandomPasswordString/MWCryptRand::generateHex/MWCryptRand->realGenerateHex/MWCryptRand::generate/MWCryptRand->realGenerate
MWCryptRand::realGenerate: openssl_random_pseudo_bytes generated 7 bytes of strong randomness.
MWCryptRand::realGenerate: 0 bytes of randomness leftover in the buffer.
MWCryptRand::realGenerate: Generating cryptographic random bytes for MediaWiki\Session\Session->getToken/MWCryptRand::generateHex/MWCryptRand->realGenerateHex/MWCryptRand::generate/MWCryptRand->realGenerate
MWCryptRand::realGenerate: openssl_random_pseudo_bytes generated 16 bytes of strong randomness.
MWCryptRand::realGenerate: 0 bytes of randomness leftover in the buffer.
[session] SessionBackend "n94eau9g0hoeo1397jtdsf281grae587" data dirty due to dirty(): LoginSignupSpecialPage->getFakeTemplate/SpecialUserLogin->getToken/MediaWiki\Session\Session->getToken/MediaWiki\Session\Session->set/MediaWiki\Session\SessionBackend->dirty
[session] SessionBackend "n94eau9g0hoeo1397jtdsf281grae587" save: dataDirty=1 metaDirty=0 forcePersist=0
User::getBlockedStatus: checking...
[connect] Connected to database 0 at localhost
MediaWiki::preOutputCommit: all transactions committed
MediaWiki::preOutputCommit: pre-send deferred updates completed
OutputPage::sendCacheControl: private caching; **
LoadBalancer::reuseConnection: this connection was not opened as a foreign connection
Request ended normally
[session] Saving all sessions on shutdown
[caches] cluster: APCBagOStuff, WAN: mediawiki-main-default, stash: db-replicated, message: APCBagOStuff, parser: APCBagOStuff
[caches] LocalisationCache: using store LCStoreCDB
[caches] cluster: APCBagOStuff, WAN: mediawiki-main-default, stash: db-replicated, message: APCBagOStuff, parser: APCBagOStuff
[caches] LocalisationCache: using store LCStoreCDB
[MessageCache] MessageCache::load: Loading de... local cache is empty, got from global cache
[MessageCache] MessageCache::load: Loading de... local cache is empty, got from global cache
[connect] Connected to database 0 at localhost
[connect] Connected to database 0 at localhost
[MessageCache] MessageCache::load: Loading en... local cache is empty, got from global cache
[caches] cluster: APCBagOStuff, WAN: mediawiki-main-default, stash: db-replicated, message: APCBagOStuff, parser: APCBagOStuff
[caches] LocalisationCache: using store LCStoreCDB
[MessageCache] MessageCache::load: Loading de... local cache is empty, got from global cache
[connect] Connected to database 0 at localhost
[caches] cluster: APCBagOStuff, WAN: mediawiki-main-default, stash: db-replicated, message: APCBagOStuff, parser: APCBagOStuff
[caches] LocalisationCache: using store LCStoreCDB
[caches] cluster: APCBagOStuff, WAN: mediawiki-main-default, stash: db-replicated, message: APCBagOStuff, parser: APCBagOStuff
[caches] LocalisationCache: using store LCStoreCDB
[MessageCache] MessageCache::load: Loading de... local cache is empty, got from global cache
[MessageCache] MessageCache::load: Loading de... local cache is empty, got from global cache
[connect] Connected to database 0 at localhost
[connect] Connected to database 0 at localhost
[caches] cluster: APCBagOStuff, WAN: mediawiki-main-default, stash: db-replicated, message: APCBagOStuff, parser: APCBagOStuff
[caches] LocalisationCache: using store LCStoreCDB
[MessageCache] MessageCache::load: Loading de... local cache is empty, got from global cache
[connect] Connected to database 0 at localhost