First you are better off replacing the two smaller splitters with one that has more outputs rather then go through two of them and the added connection as each item will contribute to loss of signal. The better the splitter, the lower the loss so don't go the cheap route on this. It is also possible that either the a splitter is bad (yes they can go bad) or ther is a poor connection or crimp of an F connector.
Yes there are power boosters available, just be aware that some of them have a limited frequency range which could affect some higher channels. Get one that covers the high end to be sure, the cost difference is minimum.
You do not mention what system or signal you are splittling but I will assume for now that it is a CATV signal (Cable TV). If you are using this for high speed internet, you also may have problems running that signal through a power booster.
There are several brands available. You should be able to locate a decent unit from Radio Shack or a better Appliance shop. Ihave also seen them at Home Depot and even Walmart (RCA brand). In any case connect the amp in front of the splitter (input) otherwise you will be amplifing only the poor signal
Joseph Golan, RCDD