Endorsements don’t decay over time. It only decay per match.
If you are playing a mode where you can’t send endorsements (eg, Deathmatch or Mystery Heroes), your endorsement also don’t decay.
Source: I quit the game for about three months and went back still at level 4. I play MH all the time and I’ve only seen it decay when I’m playing QP or 3v3. For some reason I receive a lot of endorsements in comp, probably because I only play comp when feeling more sociable, and I shotcall often.