I’ve also had this issue on two older devices, one running Android 4.4.2, and one running 4.4.4. I currently have F-Droid 1.6 on both, although from memory, I had the same problem with previous versions on these devices.
The workaround I’ve been using it to use Yalp to see if there are any updates to apps I’ve installed with F-Droid. Then when there are, I turn off the F-Droid repos, reboot the F-Droid app, then turn the repos back on again. F-Droid then detects the updates, and downloads and installs them as normal.
I just just did this and I’m in the process of updating F-Droid to 1.6.2 on both devices (as well as installing all the other updates that have been pushed since I did it last). Crossing my fingers that this will fix the issue …