Network issues with the AlienDalvik for sure in 4.1 release. Not yet present in 4.2 though. I only use the Sailfish Mail client because it just works. Signal should also constantly keep checking for messages in the background. If you want things to go similarly with ProtonMail check this out. For some rebooting the network stack in Asetukset was enough to get back internet for Android apps.
I had to always do the complete restart. 4.2 seems to work a lot better, even though it has not fixed everything that is broken.