The 2610XM should work with the NM-4E= at IOS 12.2.8T. I ran it through the online Dynamic Configuration tool, and it didn't object to that combination.
Maybe you have a bad module. I had a new NM-8AM 8-port V.34 analog modem module that kept a 3745 router crashing and rebooting. Got the replacement installed earlier today, everything's fine now.
Not knowing what you need the NM-4E= for, I was just curious: had you considered a switch that could also route IP? That 4-port Ethernet module for the router lists at US$4,000 while the WS-C3550-24-SMI switch will do static and RIP IP routing, give you 24 10/100 ports at wire-speed and two GBIC slots for only US$2,995 list. If you're only doing IP routing among several networks, it will be faster on the switch and you'll get some extra ports, too.
If you use the router for routing protocols other than IP (for example, IPX or AppleTalk), you could configure it to do interVLAN routing: set it up as a "one-armed router" over an 802.1Q or ISL trunk connection, to handle the non-IP protocols. Configure the unique network information on subinterfaces of the router's built-in 10/100 Ethernet port. Just a thought...
Hope this helps.
