Unless it's been damaged or is very, very old, it's unlikely that your Acera derailleur is the culprit. Acera is not Deore quality, but it's certainly not junk and they usually perform well. Hence the term "cheap but cheerful" when referring to lower-cost Shimano components.

It's interesting that it works fine for a while after the shop works on it. What EXACTLY are they saying they did to it to make it work? It's unclear how much experience you have working on bikes, but you should learn to adjust shifting and braking and other minor tune-up tasks yourself. YouTube is your friend. Whatever the bike shop is doing to fix it, learn to do it yourself.

The first thing that comes to mind are cables and housing. Have the cables been replaced recently? Cables do stretch a little when they're new, especially the cheaper ones. Or maybe the cable clamp on the derailleur is not holding tight and it's slipping? It could be a number of things. Your new bike shop will hopefully be able to diagnose it once and for all. It's never wrong to replace all the cables and housing on a bike, especially if what's on there is "budget" oriented. Look for stainless steel, drawn and pre-streched cables, along with high quality compressionless housing. Jagwire is my go-to source for both cables and housing, but there are a lot of other good ones.

I agree with your friend at the bike shop. If you want to change gearing for a legitimate reason (or because 1x is all the rage these days and you want to be one of the cool kids) that's one thing, but to do a complete rip-and-replace just to make your shifting work right doesn't make sense. A 3x8 Acera setup should work fine and need few adjustments.