It sounds like the battery is slowly being discharged when the tractor is sitting. To confirm this, you would need to disconnect the positive terminal, and check the discharge current with a VOM. It should be zero, with the lights off, and the ignition off. Another possible cause is a defect in the charging function, when the engine is running. Does your tractor have a charge indicator gauge?

You have probably already checked battery connections (clean, no oil on them) and any dead man switches (free of dirt). Also, perhaps take the battery to your local auto parts store. They can check it for "Cold Crank Amps" reading, tell you if it is really dead for sure, or something else is the problem.

What is the out put from the alternator on the Cub Cadet 1000?

Is it providing enough to properly charge the battery.

To check you may put the battery on a charger.