I believe there are several equally common culprits that could cause this:
- Capacitors
- Belts
- Mechanism
- Tape head (condition and alignment)
Replacing the capacitors and belt and gently cleaning the tape head is definitely recommended in any case.
1: Type in a program from the manual that's designed to run for a long time, such as the clock program from the +2a manual (page 335 of the pdf), and let it run for an hour or so.
This will let you test system stability. If the program crashes, the capacitors are the first suspect. If the system voltages are shaky, loading and saving are probably going to fail. You can of course measure the voltages if you're able, but I don't have a guide to doing so to hand.
2: Test if the Datacorder can save and load its own data.
Look inside the Datacorder window while you're using it, see if it seems to be rewinding, playing and fast forwarding correctly.
Type in one of the longer (30 line) programs from the manual and SAVE it to a new tape and then try to LOAD it again (making sure to let the tape run past the leader before beginning the SAVE). If the system can save a program and then load it again, then the physical tape system is probably okay (belts, mechanism) but the old tape you're trying to load from might be bad, or you might still have some tinkering to do with the alignment.
If the system can't save and load its own data, definitely check the mechanism in the tape drive is working and free to move, the belt is in good condition, power is getting to the tape section and all the capacitors are in order.