I'm having similar problems with my Apple Time Capsule. I used to have a Linksys WRT54GL, and it worked with no problems.

I've been doing a bit of investigation, and this is what I have discovered so far:

1. There is a basic admin interface on the cable modem at http://192.168.100.1
2. No username or password is required
3. In the admin interface, there is a log panel. I get these errors:

1970-01-01 00:07:43	3-Critical	D001.0	DHCP FAILED - Discover sent, no offer received
1970-01-01 00:00:16	3-Critical	T001.0	SYNC Timing Synchronization failure - Failed to acquire QAM/QPSK symbol timing
1970-01-01 00:00:11	3-Critical	T002.0	SYNC Timing Synchronization failure - Failed to acquire FEC framing
1970-01-01 00:00:11	3-Critical	T001.0	SYNC Timing Synchronization failure - Failed to acquire QAM/QPSK symbol timing
1970-01-01 00:00:11	3-Critical	T002.0	SYNC Timing Synchronization failure - Failed to acquire FEC framing
1970-01-01 00:00:10	3-Critical	T001.0	SYNC Timing Synchronization failure - Failed to acquire QAM/QPSK symbol timing
1970-01-01 00:00:05	6-Notice	M572.0	Ds Lock Failed - Reinitialize MAC...
1970-01-01 00:00:03	6-Notice	M571.1	Ethernet link up - ready to pass packets

4. These log messages tend to suggest that the cable modem is having signal errors.

The other interesting thing is that the cable modem has a configuration panel, and there is a DHCP server checkbox option. It give you this explaination:

The SURFboard cable modem can be used as a gateway to the Internet by a maximum of 32 users on a Local Area Network (LAN). When the Cable Modem is disconnected from the Internet, users on the LAN can be dynamically assigned IP Addresses by the Cable Modem DHCP Server. These addresses are assigned from an address pool which begins with 192.168.100.11 and ends with 192.168.100.42. Statically assigned IP addresses for other devices on the LAN should be chosen from outside of this range.

So, my current theory is:

1. All is working well, then...
2. The cable modem has a "random signal moment"
3. The cable modem detects that it is "disconnected from the Internet", and...
4. It enables the DHCP server option
5. My Apple Time Capsule doesn't like this
6. Somehow, the Time Capsule looses its known route path to the "default gateway", and is unable to recover

What is interesting - when my Time Capsule is in a "can't surf the internet state", I can still connect to the admin interface on the cable modem. I would suggest that this points to the fault being related to not being able to resolve a route to the default gateway.

So... I have unticked the DHCP server option to see if this helps to resolve the issue. The problem is that I'm only getting the "can't surf the Internet" state once every couple of days. So, diagnosis can take some time.

Further reading available here:

Google - http://www.google.co.nz/search?q=SYNC+Timing+Synchronization+failure+-+Failed+to+acquire+QAM%2FQPSK+symbol+timing

Apple Forums - http://discussions.apple.com/message.jspa?messageID=7319599

Cheers

Nigel
http://www.abletech.co.nz/