We are experiencing some complaints of slow response times from one access switch out of three 4507 access switches that connect to a core/access 6509 switch.

Difference is the other two 4507 switches have fiber uplinks utilizing the two supervisor modules connecting to the fiber connections on the 6509 supervisor modules providing redundancy between the two sup cards.

Seeing how there are only a total of 4 fiber links between the two supervisor cards on the 6509 we had to use copper line cards to uplink the third 4507. Seeing how we still wanted redundancy we picked the second port on card 1 and card 2 for uplinks on the 6509 that plug into the 4507 that sits right next to it.

So, can a port-channel with a port from two different line cards be a member of the same port-channel or do they need to be on the same line card?

To better answer that question is your 4507 access switch running as a layer2 switch or layer3?

As a layer 2 switch I don't believe you can have your port-channel on two different copper line cards. You can have up to six ports on the same line card in your port-channel.

As a layer 3 switch you can but you need routing enabled and create two different point to point links.

check for buffer drops on the interface (on both sides of the uplink)