Can AVR or loose speaker wires cause AFCI to trip?
A properly functioning audio/video amplifier should not cause AFCI trips
AFCIs work by monitoring the waveform of the AC power signal and looking for a particular type of distortion that is indicative of an electrical arc, and cutting power if that is seen.  This doesn't play well with every device -- some devices, such as brushed motors, have small electric arcs inside as part of their normal usage, and others such as dimmers, consume power in such a weird and inconsistent way that they can fool the detector.
However, none of these concerns apply to typical audio/video systems like you have.  In fact, audio amplifiers have quite a lot of filtering in the power supply section, to make sure that noisy incoming power won't be heard in the speaker output.  This same filtering means that the way audio amplifiers draw power is also very clean, and won't make any unusual noise on the AC line.  The video section of the unit is all digital electronics, and isn't any more likely to trip an AFCI than a regular computer.
Most likely, something is wrong with your AVR unit
The fact that the trip sometimes happens right away, and sometimes happens after a while makes me think it's likely your AVR does indeed have an intermittent fault internally.  My guess would be an insulation breakdown in the transformer somewhere.  Since devices this complex sometimes have several transformer windings for independent power supply rails, such a fault might not even cause the amplifier to stop functioning completely, but it is a real problem that the AFCI might detect.
Double check your grounding
This is a little more esoteric and less likely to be your problem, but for completeness I'll include it as well.  While most electrical equipment uses the ground wire only for safety purposes, audio equipment frequently also uses it for shielding of audio signals.  Often, the shells of all the HDMI and RCA plugs on the back are connected directly to the earth ground coming from the wall plug.  This then gives lots of opportunities for unusual signals to couple to the ground wire.
How does this affect AFCI?  If everything is wired correctly, it doesn't at all -- the AFCI doesn't look at the ground wire.  But if your outlet was wired with a bootleg ground, i.e. where the ground terminal is also connected to the neutral wire, then the AFCI will be able to see that ground noise, and it could interpret it as an arc.