My phone keeps unpairing with my watch when it gets out of range I'm using a Pebble Time smartwatch (on Pebble OS v3.13) and Xperia M4 Aqua (on Android 5.0).

Whenever my phone gets out of range it unpairs with my pebble. I end up needing to forget my phone from pebble and pair again with my phone. This is becoming frustrating, and I can't find anything relevant on my watch's help page so I think that this is a problem with my phone. How can I fix it?
From the extra information you provided in the comments, it would seem as if the Pebble app is malfunctioning, and if it isn't, pebble support will be able to direct you to who can fix this for you. While they can be a bit slow to respond, they are very good.

To contact pebble support, open the pebble app and tap the drop down menu on the top right corner (3 dots). Tap the "support" option. Choose "contact support" from the list of options that open after tapping support.