Just to give you company: On my 655 using "http://dlinkrouter" does not work either. But I really don't care, since typed URL's are autocompleted nowadays

My former routers (Asus, Linksys) also suffered from the same, but suddenly responded once in a while.
By no means this tells you the device is defective. If you can connect to a computer by IP address and not by NetBIOS name, the problem is with Netbios name resolution.
You can artificially make this happen though, in Windows by editing the HOST file (IP may vary with other configs):
192.168.0.1 dlinkrouter (or in your case 'dlinkap')
The Netbios nameservice will use the HOST file to identify the designated IP by the name. It requires (in Windows) the LMHOST to be active.
I'm sure Mac also has an equivalent (not a creative guy, sorry).
The router or AP does is not DNS server, so name resolution does not take place inside the router. The router will only
forward the request to your ISP's DNS server.
The fact that 'DLINKAP' does not work is most probably an issue with the client. This can be caused by a number of reasons. It could be a Netbios broadcast issue (which can not cross other routers/AP's in the LAN), which settings can also partially be manage from the router setup (on the 655 it is on: http://192.168.0.1/Basic/Network.shtml)
Any way... I need to go to sleep (Europe) so I found you an article on these kinds of problems with Netbios: http://articles.techrepublic.com.com/5100-10878_11-5034239.html.
Takeaway: NetBIOS alone should not give you many headaches. Unfortunately, when NetBIOS problems occur they can be difficult to detect. Understanding how NetBIOS works is the key.
Let me know if your issue was solvable by any of the 5 solutions provided (partially also covered above).
Conclusion so far: this issue does not indicate a broken router.