Cisco Switch Ports resetting themselves after disconnect and reconnect of Layer 3 uplink

Prefacing this with, "I don't network, so talk to my like I'm five."

In our camera system on multiple floors in one building (4 total switches), we needed to move the layer 3 routing config from one switch (Cisco C3560G - SWITCH A) to another completely new switch, in a different room (Cisco 2960X - SWITCH B). Re routed the cables so there was an uplink to our corporate network, as well as to the ORIGINAL layer 3 switch, which has had the IP routing config removed from it now. It's only uplinks are to the new layer 3 switch and to the other floor camera switches.

On SWITCH B, if we unplug the uplink to SWITCH A, all cameras we expect to drop connection do, and the ones we expect to stay up stay up. When we plug the connection back in, all of the switch ports reset themselves immediately, knocking all cameras offline, and then reestablish connection in 15-30 seconds or so.

Whats going on?