Router connection/performance limitations

I have a Trendnet TEW-639GR router tied to my cable modem. I have used this pair for the last year and a half with little issue. I recently upgraded my TV which caused me to redo my whole entertainment system. As part of that make-over I decided to wire in all of my networkable components. Now after adding all of these items to the network on top of the large number of items I already had wired and wirelessly connected, I have items that are not seeing the network until I unplug and re-plug to the network. Is it possible that my router is not able to handle the large number of connections that I am throwing at it? Is that what may be causing these drops?

My connection list (approximately):
Wired -
2 desktops
XBox 360
PS 3
DirecTv
TV
Windows Server
Slingbox

Wireless -
2 laptops
2 iPod Touches
iPhone 3
PSP
Buffalo Link Theater

Note that all of these are not in use at the same time but it is typical for there to be multiple items using the network at any time.

Thanks for the input.

How is it possible that you have 8 wired devices connected to a router with only 4 ports? I'm guessing you forgot to mention an additional router you added in the mix which could be causing DHCP problems. If that's not the case I'll need to know how these are all connected. Are you simply plugging and unplugging things when you decide to use them?

As for the number of devices, I would expect wireless issues because usually you can only connect so many wireless devices at a time, but it depends on the router so look up the documentation on yours for that.