If you have multiple VLANs, then it sounds like maybe one or more of the VLANs is not being carried across one (or more) of the switch-to-switch links. Check your config to see that all your inter-switch links are VLAN trunks. Then check to see whether you're manually removing any of the VLANs from the VLAN trunk. Remember, Cisco does a Spanning Tree Per VLAN; so each VLAN has to have its own loop, otherwise it can get isolated from the Root Bridge when there's a link failure in the right place. (Or wrong place, depending on how you look at it.)
Also, if you're using 802.1Q encapsulation, make sure that the native VLAN on each end of a switch-to-switch link is the same.
How are you configuring your network so that it specifically blocks the link between your 4006 Backup Root Bridge and the bottom 2950G-24 in your picture? Without human intervention (for example, manually increasing STP costs on certain links, or using UplinkFast on a switch), STP would naturally want to block the link between the 4th and 5th 2950T-24, counting down from the top in your pic.
For what it's worth, the way your switches are chained together is creating a Network Diameter of 11. STP's Max Age and Forwarding Delay timer default values are based on a Network Diameter of 7. So you may also be having some reconvergence timing issues, too. If you are restricted to this topology, and all the other stuff checks out, try extending the Max Age and Forwarding Delay parameters on both your Root Bridge and Backup Root Bridge. (Configuring it on the Root Bridges, it will propagate to all the other switches.) Remember to do this for each and every VLAN.
Values to try: if your Hello Time interval is the default of 2 seconds, then MA=28sec and FD=21sec. Reconvergence will take place in 42 to 70 seconds, vs. STP default 30 to 50 seconds. If your HT=1sec, then try MA=24sec and FD=19sec, for a reconvergence of 38 to 62 seconds. Yes, it's a painfully long time -- but until you shrink that ND, that's what you're stuck with.
Hope this helps.
