The consistent thing bugs me.
If it was random dropout times then it would be like some router units I experienced in the past. Downloading the latest firmware from the manufacturer and loading it on the router fixed a good number of these.
If it is 15 minutes, always, on the clock, every time. This keeps me thinking you have a software setting somewhere buried as a candidate. My mini is set to sleep every 15 minutes, but it never has bumped my internet / wireless connections before.
It still might be worth a check of the Energy Saver tab in Preferences and turning them off for a test if they are on.
How did you set up the network parameters initially on the mini--I think we have eliminated the router from the loop with direct cable modem connect.
Jan J.