Actually figuring out when the last time a GM logged in is very easy. On the Team Owners list on Fantrax, it lists the date of the last log-in.
I do think there should be a minimum number of log-ins per month. At least check your team twice per month or something like that.
It is easy to figure out when they last logged in, but if as has been suggested, you need to login 20 times per month, that is not easy to figure out. You have to go in daily and tick off who was there that day or record the last date for each person every day. Twice a month is easier, but you still have to be on top of it, because if someone logs in on the 14th and again on the 16th and whoever tracks this doesn't notice it and only sees at the end that when they checked on the 12th they hadn't logged in and when they checked on the 17th they last logged in the 16th and then not again for the rest of the month, it just makes a big mess and headache to manage. Easiest to say once per month or once per two week period or once per week or something that can be done every Friday or every 15th and last day of month or just the last day of the month.