Running forums is a difficult task, often you need staff to help you run a forum so that you don't get run down dealing with all the problems that can arise on your own. Unfortunately staff will become inactive whether it be due to personal reasons or just because they are no longer interested in being on your forum and when that happens you have to find the best way to approach that and deal with that.
I always tell my staff that if they are inactive for a period of 7 days I will contact them and ask if everything is okay usually by email so that I know they may receive it if they have not been active on the forums. If I do not get a reply within 3 days I will then take action and demote them. I understand that everyone runs into personal problems in life meaning forums are not their main priority which is fine but when you do not hear from your staff within 10 days I guess the only action you can take is to demote them and then deal with it if you hear from them after that.