Start with the modem's signal stats. Perhaps they already are, or they are close to being out of spec and intermittently they go completely of spec. Try getting them here http://192.168.100.1 or here http://10.0.0.1
Please post the *Downstream Power Level*, the *Upstream Power Level*, and the *SNR* (Signal to Noise Ratio) numbers.
What is the exact make and model number of the modem ?
Is this a WiFi connection ?