My guess would be that the degradation of the tape over time has made it such that the comparator in the datasette doesn't trigger properly to convert the audio signal to TTL, and you don't get a good data load.
My advice would be to record the tapes right away to digital audio files. I believe there are some tools to convert audio to .tap files, I don't recall the name now but will look it up. If you get it to a tap file, and can successfully load onto an emulator, then you can regenerate a clean audio signal again from the tap and re-record onto a new tape. If there are issues converting from wav to tap, some filtering of the recorded signal might help - probably boosting the overall level and filtering out the higher noise frequencies would be good. But most important would be to record it as soon as you can to capture it before it degrades further.