So with the distribution amp removed, everything comes in, but only most of the time. Did I get that right?
Could be overload from a near transmitter. Could be that their just too weak during a portion of the day. Normal daily propagation cycle.
In order to take an educated guess as to 'what's what' would have to know the signal levels you're in, and the specifications of the antenna(s) and amplifiers used.
But you should be able to figure out if it's overload by taking out an amp when a signal disappears, If it's overload, it should then come back in. It wouldn't if it's just too weak.