I have a problem with several c2950 switches responding slowly on their management interface (Ping 500-600ms, slow Telnet session). The location has 23 switches (2x c3750, 6x c2960, 15x c2950). All switches are in one VTP domain (c3750 are servers, c2950/c2960 are clients), default VLAN1 only. After adding 2x c3750 and 4x c2960 (included in the total mentioned before) and switching to rapid spanning-tree some of the c2950 (not all however!) now respond very slowly on their management interfaces. The LAN topology is NOT as recommended by Cisco... In past years buildings have been added, connected by fiber. There are redundant rings and daisy chains in the topology. All switches are connected through their Gig-Interfaces with fiber.
I haven't found anything about such an issue, perhaps somebody knows these effect.
Then this could well be your problem. If everything is in vlan 1 then a broadcast by one device has to be handled by every single device in your network including all the switches. Now switches deal with most things in hardware so that ordinarily wouldn't be a problem but a lot depends on the traffic and some types of traffic have to be processed by the switches main CPU.
I think you should look to use vlans within this branch office because by the sounds of the number of switches there you have far too many users to put them all in one vlan.
In addition the daisy chaining could be causing a problem as well depending on how it is actually set up. How is your STP configured, have you configured an STP root or do you just leave it to the switch priorities ?