as stated in the topic, i started recently to have this problem.
Some app updates (torrent client, kiss launcher, odyssey) force F-droid to close and don’t install.
Another app recently added (paper launch) has the same behavior.
In addition, if i manually download the apk files when i try to access the download folder, file manager suddenly closes. I have to manually remove the apk files by connecting device to PC and using PC file manager.
I already reported this on the following thread Several apps caused bootloop on Cm 12.1 but since i don’t have CM and in my case it’s not a bootloop issue i preferred to open a new topic.
I have Android 5.0.2.