What is the name of the program that allows a Reservist to do approximately 30 days of orders to then not be required to attend drill?

Go to the HRC website and click the My Records tab, then click the Tools tab. Next, click vacancy search and you will see the option for IMA. Finally, fill in the information about your MOS and what state you are looking for and it will give some option along with the contact information.

Loom into the IMA program. It is not for all MOS's and paygrades...

I don't know about said program but I have heard of some instructors using all their UTA's in a month or two and not having to drill. If your unit is willing nothing says you have to drill weekends, you have 48 UTA's per year. When I was in my old unit we had several soldiers who RST ed allot during the week because they needed the bodies, the unit had allot of equipment etc.