Nobody loses fights. That was suggested by others, but I don't like this approach, as it does not help much.But that leads me to another question: let us say they loose 50 fights every hour from 159/160 but what if they are in front of my HQ and we have also 124/160 so far, will we both loose fights? And assuming they loose 50 fights every hour (and 1 hour is much to long, should be every 15min) will they be able to do 50 fights to bring it 159/160 again ?
My solution is, that the needed fights will decrease every hour. Lets say it will decrease by 10 every hour. This means after one hour the province will only need 150 progress, after 2 hours 140, ... after 8 hours only 80. The progress guilds made will stay, so if you have 145 progress and don't do anything, after 2 hours you will conquer the province automatically. If 2 guilds would get the sector the one with the highest amount of progress will get it. If both have the same amount, the province could go to the one lowest in the current ranking or simply random.
Also, of course the numbers can be tweaked a lot. They are just my suggestions, but I am of course no Game Designer.