Yes the Microflow Timer can be used, however to have it refresh your value you would need to do the same as what needs to be done in your initial microflow: refresh the correct object. This most likely is to blame, and where you should seek the solution. See if refreshing the context object does the trick.
I had also problems with client not refreshing.
The solutions was quite simple. The problem was I re-opened pages that where already opened (like overview pages). I changed it back to close pages where I could, so I had no double opened pages anymore.
Advice, be strict with opening and closing pages, so you only have one active client page, this solved my refreshing problems.