Too right this is a very odd problem. Here is a suggestion as l have no idea what could be the source here, why not remove all variables from your setup? (update the firmware on all your Linksys routers to the most recent firmware, or just double check that the default settings on the routers are default across boss. You could be missing something very small). You have though provided the best possible solution to your problem: replace the Linksys routers with another brand.
Too bad l could not give you any concrete help. Please let us know what the ultimate solution is when you get one.
Best of luck.
Check with your ISP…We had this problem as well, Our ISP didn’t take responsible to start with until everyone was complaining about the issue similar to yours…We were running on SERVER Small Business and installed new modem, configured Smooth wall and all that doing our ISP finally admitted they’re experiencing satellite issues. We only have one ISP in our region.