When you have connectivity, what do the modem's signal stats look like ? Try getting them here; http://192.168.100.1
Please post the *Downstream Power Level*, the *Upstream Power Level*, and the *SNR* (Signal to Noise Ratio) numbers.
Is there a router in the mix ?
It really would be helpful to see those signal stats..
In a self troubleshooting effort to try to obtain better connectivity, check to see if there are there any excess/unneeded coax cable splitters in the line leading to the modem that can be eliminated/re-configured. Any splitters that remain should be high quality and cable rated for 5-1002 MHz, bi-directional, and no gold colored garbage types like GE, RadioShack, RCA, Philips, Leviton, Magnavox, and Rocketfish from big box stores like Home Depot, Lowes, Target, Wal-Mart etc. Splitters should be swapped with known to be good / new ones to test
If there aren't any unneeded splitters that can be eliminated and if your coax wiring setup can't be reconfigured so that there is a single two way splitter connected directly off of the drop from the street/pole with one port feeding the modem and the other port feeding the rest of the house/equipment with additional splits as needed, and you've checked all the wiring and fittings for integrity and tightness and refresh them by taking them apart then check for and clean off any corrosion / oxidation on the center wire and put them back together again, then perhaps it's best to book a tech visit to investigate and correct.
Good luck ! Post the stats when you can.