I agree with EMP. You have your staff rank to help out on the server whenever help is needed when you are online. If they don't perform when there are alot of F1's, then they deserve to be reported in a way like this. When you apply for staff you should consider it by yourself first: Do you really want the rank? Will you perform the work that is required? If not, then I strongly suggest to re-think applying. At the same time I can also imagine their view. Some staff just want to RP sometimes, which in my opinion is nothing wrong with, unless there are 9 F1's waiting.
Anyhow, here's a suggestion for EMP:
Are you able to make a system that allows to tell how many F1's a staffmember did? This system will be reset after each DarkRP meeting, so you have a full week of data. This makes it really easy for the leadteam to pick out the inactive staff and have a talk with them, or demoted if it's needed. You can also make some kind of rewarding system which gives the staff finishing the F1 around $10,000. don't know if this is possible to create, but I just wanted to help out a little.
PS: There are some staff doing a great job, for example AllThatJazz. Keep this up guys! Your work is appriciated by many people.