Common problem with old receivers - oxidized contacts. Get a can of contact cleaner, probably available at Radio Shack, but certainly available at better electronic parts jobbers. Remove the receiver's case and spray each switch and pot while turning/rotating each switch/pot.
If the receiver has dirty contacts, this may help for a while (maybe a year or so), though mechanicaly cleaning each switch works better. I do this as a hobby and it can be quite laborious.
Some receivers have a relay which powers on the amplifier section after the power supply. If your receiver has such a relay, you may hear it click on soon after turning on the receiver. Check it - if it is a sealed unit or has gold plated contacts, it should be OK. Otherwise, use contact cleaner and very fine sandpaper (real emory cloth works better) to clean the relay contacts.
The RCA plugs used for external connections become oxidized too, though they don't usually cause signal dropoffs. Easy to clean - pull the RCA plug out a bit and rotate it around in the receiver's jack.
You may have an electrical problem with the receiver, though your symptoms as posted would lead me to suspect oxidized contacts.
Good luck.