I will post my solution here to anyone who has come across this issue. I have observed for a couple of days now, and I can confidently say I have figured out what the problem is. The ethernet cables weren't the issue. Every time the router lost power or connectivity for even a second (whether there is a power outage, router is upgrading and needs to reboot, or ISP is having issues), the switch would only allow speeds of 100mbps; it's like the router was the one limiting the speed, not the switch. The fix I found that worked every time is to simply unplug the ethernet cable connecting the router to the switch ON THE ROUTER not the switch. Simply unplug at router, then plug back in and it would correctly auto negotiate to gigabit speed. Hope this helps.

You would not believe it, the speed has been stable for 2 full days now. I only unplugged the ethernet cable and moved it to port 2 as port 1 is for the router. I don't know if this made a difference (shouldn't because the switch should have memory of the MAC addresses on each port in the MAC address table and it shouldn't matter what port the two items are on). I am starting to think that it really was the ethernet cable. It seems that although the ethernet cable was clicked in, if I jiggle it around it can loose its gigabit speed for whatever reason. One more thing, when I changed out the switches I went from a Netgear GS108 to the Linksys SE3008. I guess the chipset is probably not the problem, but if more issues continue I will try the TP-Link switch you recommended. I appreciate the quick reply and thank you!