I would highly recommend watching some videos from Park Tool
& RJ the Bike Guy
Also the Shimano manual
DM-GARD010-00-ENG.pdf (shimano.com) may be the best place to look. Best to learn how to work on them yourself. It will come in very handy and save you multiple headaches and trips to the bike shop. Not busting your backside, just giving good advice. Since you say the cable slipped in the clamp once already you should check to make sure the clamp bolt is tight and if you have the coated cable that Shimano sometimes uses, scrape off the coating where the clamp is. A slipping cable will have the exact symptoms you describe but not the only possible issue. If whoever setup your bike didn't make sure all the shifter housing pieces were solidly inserted into the various stops at the shifters, downtube stops, and each end of the derailleur loop it could still be creeping until it butts up against the stops. Check these and let us know if you still have problems.