Altenators have a diode pack in them, usually 3, if one goes bad the alternator loses 1/3 of its amperage capacity, The diodes job is to only let current flow in 1 direction down a conductor, if its bad it may be a open circuit or it may cause the alternator to draw current from the battery when the engine is off. (does not sound like your case because you can get 3 weeks out of a charge)
You need to check the alternators voltage with yours lights, heater etc all on to see if you have @ 14.5 volts, if your under 14 volts your battery will not fully charge. It is also possible the altenator does not work at all, but unlikely you could get 2 weeks before you have to charge.
Certain models (ie 753 but not 763 or 773, that way the dealers get the full info from a complete manual set, but if you buy just your 773 manual you may be SOL) of the bobcat service manuals have a complete testing section for the alternator
Download some of the manuals for the other models and have a look
Delco is still you best bet, reliable, cheap and cheap to rebuild. My local stater alternator shop laughed when I brought my Mondo in. he said "Son, we don't fix those!" The parts were more then the Delco was outright
Ken