Help wth TPLink WR841N router

I installed the above router to repleace a Netgear WRN2000 router that I use for several years and hardly had any issues with until recently. But since installing the TP-Link, I have had frequent disconnects from my network and have had to reboot the modem and router almost daily. I guess my question is, is there some sort of diagnostics I can do on the router to verify that it is the router and not an issue with my modem, a Motorola Surfboard SB6120? I'm ready to ship this TP-Link back to Amazon (it's only been about a month) but just want to make sure I am correcting the problem here.

Update the router firmware to see if it improves anything.
Test the TPLink router with known good ethernet connection (ex. your friend's house?) and see if it keeps the connection for one day?

Do the above tests with WNR2000 router to boost the confidence level.

You might be able to find some info/user reviews/complains on the modem on dslreports forum.

I agree, upgrade your router firmware.

When your connection disconnects are you still able to connect via wired through the router?
You can always connect straight to the modem, and see if your connection is more stable?
Are you on the same wireless channel?
Did you get security setup properly when you setup the new router?

Check if the cables are worn out. Replace them if you can.
Try a different computer.
Bypass the router and connect directly to the modem.
Could be ISP wires, but more likely a lemon.