Please do not disconnect the battery while the engine is running.

Is there a reason for you doing this?
Also it will be helpful if you explain in detail what happens when the problem occurs.

1. Make sure the battery connections are clean and tight.
2. Charge the battery, slow, low amp charge is best. Battery should have over 12 volts at this point.
3. start the engine, check voltage at battery, should be about 13 to 14.5 volts.
4. If voltage with engine running does not increase, the problem is either a worn out voltage regulator (on the back of the alternator) or worn out alternator. This is assuming that all the electrical connections are good.
5. If the voltage increased properly with the engine running, you should have the battery properly load tested and the cells checked as mentioned in above post.

PS. I think you may also need to check for excesive current draw.

Good luck,
Acky