Unlike the old days, when splitters could cost a cable company $, most providers that have been digital for a while (fios providers especially) compensate for signal attenuation in their signal strength. You should be able to split 3 ways minimum with no issues (a friend has a 1x8 without an amp). Unfortunately, that's not a universal standard.

My first test would be to swap out the cable coming from the splitter; second, unplug the other connections on your splitter, and test your cable on each output; third, run directly from the demarc to your box. This should tell you if it's the cable, the splitter, or the cable company.