What do the modem's signal stats look like ? 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 ?