Older tape can become sticky as the binder glue that holds the oxide to the tape's backing gets gooey with age and can literally bring a machine to a full stop because of the added resistance. Tapes can be rescued temporarily by baking them to in effect, dry that glue back to a non-sticky state.
We have many threads here on this topic. Read them!
Could be sticky tape, could be non-oiled bearings heating up can be a stretched belt or non oiled capstan motor and might even be a glazed capstan shaft slipping. You do not list the model number so help is limited as we do not know of what we are speaking about.
I am sure I could help as I have worked on these 40 years at least so far.