DTV Reception Good Except When Windy

I have a new "Terk" brand indoor antenna connected to my DTV converter box. Reception is good, but when it's windy, the signal goes in and out (presumably because of tree branches blocking the signal). The standard answer for my problem is to get a roof antenna. But the same towering tree branches could still block the signal.

Does it make sense to use a T-connector to connect two antennas (spaced several feet apart) into one TV? That way, if swaying tree branches are blocking the signal to one antenna, the other antenna would still get the signal.

What is the best solution for getting reception on windy days?