One problem might be that the AVR's subwoofer output level is too low. The subs are probably set to auto-on where they need a certain level of signal to activate and stay activated. If that signal is too low, the subs can just end up shutting off during a program sometimes or seeming to need a large signal to wake up. Make sure the subwoofer out or LFE out is not set too low.
But yeah, if you want to watch movies and have a modern TV, disc player, or streamer, you will want an AVR with HDMI connectivity.