Greetings, and welcome.
First, some questions: what printer and what build surface (glass, magnetic mat, steel sheet, carbon fibre)?
Without an answer to the above, I’ll tell you what happened to me (having started in November) but you have to keep in mind that if your printer is different, some of what I suggest may not apply in quite the same way.
First off, I presume you are aware of the vital importance of tramming (“levelling”) the bed? I have always found that a single sheet of printer paper is good enough to get the spacing right, although others swear by post-it notes (apparently thinner), or mechanic’s feeler guages (definately more precise).
I also presume that you are measuring the the height at all four corner and in the middle of the bed. If you don’t do that, you can have a case where a print starts to stick nicely at one corner/side and starts to lift off on the other, because one side is set up correctly and the other wasn’t.
Moving on… I bought a Creality Ender 5 Pro, which has a magnetic bed. It worked beautifully at first, but after a few months of scraping prints off, the surface, which initially had a texture, started to get smooth in spots. I ended up replacing the bed, which solved the problem, but of course it keeps recurring. I later switched to glass plates, which printed beautifully, but which was not borosilicate glass. That type of glass contains boron-trioxide which significantly lowers the glass’ thermal expansion. Those sheets worked for PLA, but when I tried printing higher-temperature Polycarbonate, they shattered. I now print on Carbon Fibre which has the surface finish of glass and so far hasn’t had any problems.
So, your problem could partially be a worn build surface.
The one negative thing I can say about carbon fibre, is that PLA doesn’t stick well to it at all. I have to use a thin layer of glue stick, but then that layer will last 6-10 prints before needing to be renewed. Also, if you try a glue stick, absolutely go for Elmer’s. It doesn’t have to be the purple stuff, which worked fine, but the slightly cheaper “all purpose washable gluestick” literally requires me to hammer the spatula (that came with the printer) at the bottom edge of the print to get it off. I have no problems with adhesion now. By the way, stay away from the Staples house brand glue stick - it’s absolutely useless for 3D printing.
So a washable glue stick may solve your problem.
Be aware that filaments are absolutely not created equal. Different brands, and even different colours within the same brand, can require printing at different temperatures. Filament can be finicky.
I’ve never tried PETG, personally, so I can’t comment on it.
As for filament that isn’t going through the exturder, this could depend on the model of printer. Some printers have plastic, not metal, extruder motor assemblies. The plastic ones have a well-documented history of cracking under the stress. When they do, the can no longer grip the filament as tightly as they should. The symptom is that the filament randomly stops moving.
I’m presuming here, that you’ve already checked, visually, to confirm that the extruder is, in fact, turning? I actually printed an extruder “wheel” that pops on the end of the extruder shaft and gives me a visual indication that the extruder is moving, even at a distance.
If the extruder isn’t moving, it could be a loose cable. My style of printer isn’t prone to this, but printers that have the extruder mounted on the carriage are obviously going to be moving the extruder cable along with the carriage and that can be enough to start wiggling it loose over time. Check your connections if that applies to you.
Overheating of the extruder motor or the extruder motor driver (on the controller board) can also be an issue, but I doubt that cookie cutters are taxing the system hard enough for thermal issues to arise.
Another possibility is the tension on the extruder arm. That’s the arm that you squeeze to load a filament. The tension comes from compressing a spring that is pre-stressed by a screw. That screw can work loose over time, reducing the pressure on the tensioner which in turn reduces the grip on the filament.
If you’ve been doing a LOT of printing, it’s also remotely possible that the extruder gear itself is grinding down, although that usually takes months to years.
As a newbie, I would also highly suggest you visit Teaching Tech’s calibration site and read every page starting with the introduction. It will take several hours to complete all the steps, but you will end up with a well-tuned machine when you’re done.