I have a 2004 Volkswagon Beetle. Both turn signals went out at the same time; i change the fuse and they worked again - for about two signals then stopped. Just to make sure, I changed the fuse again, and the same thing happened. The signals work two /three times then both (left and right) stop working.
Sounds like a short, replace the (very cheap bulbs) and clean the connections when you do. it’s worth a shot for $3 and a little time, but is likely a short in the wiring
Try cycling the emergency flasher switch to see if that makes any difference. The power for the turn signals runs through it.