Apps suddently stopped sending notifications on my Nexus 7 (2013) running Lolypop 5.0.2
A suggestion for a solution could be to first restart your phone and see if this helps (I have experienced many different bugs on the newest Lollipop that were fixed by simply restarting my phone).

If this does not work, try a reinstall of the app - if possible and you do not lose important data from that of course. 

If the second option works, it could have been due to the 'optimizations' that Android performs on apps when updating to a newer system version (my best guess).