Well I am no electrical guru, but I have been learning while getting the issues with my 48 solved... but I will give it a shot
1. If you have a magneto then there are no issues about running the tractor without a battery. Since you are having issues then you do not have a magneto but the battery ignition package or essentially a distributor. If you had a magneto, a battery is superfluous except to assist in starting.
2. So, if you have a battery ignition then you probably have issues with the voltagte regualtor I think. Rather inexpensive fix I imagine. NAPA has em but cannot remember the part number at the moment.
3. If you left the ignition on and there was power to it, then possibly the points are a bit burned.. but that would make starting difficult or it would not start at all. Same with the condesor.. might be intemittent, but more likely it would be toasted.
It sounds like the battery is not getting charged...
One of the electrical guru's should see this soon.. I hope. In the meantime I would suggest reading the GSS-1411 Service Manual on the server or using one of the other electrical manuals there to help diagnose the problem There are a couple of really good IH manuals there.