media1's answer reminds me that what is happening is not always what we think is happening.

When a splitter goes bad and you replace it, have you ever tried the old splitter again just to see what happens? If you replace the splitter the next day and signal conditions are better, your new splitter might look like it is working...but the old one might, too, if you tried it then.

And he is right -- if you remove a 4-way splitter you get four times as much signal to the one TV that is connected; signals on the edge of being poor quality might work directly but not through a splitter...sometimes.

You need to do some testing to take that "sometimes" out of the equation.

As for the preamp, I once used a satellite preamp with a guy's signal because he insisted on it. The signal level (which is really signal quality, and not necessarily related to signal level) went down some fifteen points when we put the amp in the line.

So back up a few steps. Connect the antenna without the amp to one TV and see if you always get good reception. If the splitters seemed to fail at particular times of day, check station signal levels at that time of day to see if the signal varies. Then, knowing that a 2-way splitter reduces a signal by about 4 dB (3 would be in a perfect world) and a four-way by about 7 or 8 dB (6 in a perfect world), put in a splitter and see if things work without the amp.