Hard to say.
Are you using Linksys firmware or alternative firmware in the WRT54G?
You don't have 54Mbits/sec bandwidth. That's the connection speed. Assuming ideal conditions, you won't get more than about 25Mbits/sec in thruput. Typical is about 1/3 to 1/2 of the connection speed. Dive into the status screen on the routers and radios and check your connection speed. My guess is that you're probably saturated at
10-12Mbits/sec.
It's failing the "windows browser election" abomination.
There you have it. You're saturated. You're at or above the available bandwidth limit and are starting to drop packets. Since the TTL is artificially short of pings, they'll be the first to disappear.
It's a matter of signal strength and distance. Some computahs are closer to each other, or closer to the WRT54G that's next to the gateway. Check the connection speed. It will give a good idea of the path quality.
Linksys WRT54G are quite good. Stay with them. There's nothing much wrong with the topology. However, you're making things difficult using ad-hoc. There's no central controller, so some things just tend to get lost. There's also no bandwidth control or traffic management.
I'm not sure switching to infrastructure is going to help. It really depends on your traffic requirements. If you're cameras are running a "push server" which send frames as fast as the traffic will bear, you will be saturated no matter how much bandwidth you give it. I'm not familiar with the Axis 2100 but there should be some kind of frame rate control on the push server. Slow it down somewhat and you'll probably be all right with the existing arrangement. Also, so some measuring of bandwidth used. Try it with a wired ethernet connection instead of wireless and see how much bandwidth it really wants.
I suggest you look into alternative firmware for the WRT54G. One of the features is a crude form of bandwidth management. You can prevent the cameras from hogging all the bandwidth. See the various releases on the Sveasoft site for details.
All these wireless networks are bridges that work on ISO layer 2. They don't know anything about TCP/UDP/ICMP/whatever that are on ISO layer 3.
I have a customer with 3ea old Axis 210 cameras. I can totally fill up his outgoing DSL bandwidth (384Kbits/sec) with these cameras using the built in push server. I forgot exactly what I did to slow them down, but they're now demand driven and no longer pose a problem.