Ever since I've started using Meraki AP's at home, my internet goes down frequently. I didn't have this problem when I was just running a residential Apple router. I'm using a standard Linksys router with my MR42 and I have not changed anything with my ISP service. Sometimes, it will come back up on its' own after time. Others, I have to unplug everything for a few minutes and boot back up. I'm assuming I probably need to upgrade to a better router?
If its just a standard home router does it have PoE? If it does it still might not have enough power to run the AP. And you might be looking at double NAT or a port forwarding issue.
When you say the internet goes down, is it just the SSID being broadcasted by the MR is no longer seen, or not passing traffic? Does the Lynksys router stop passing traffic as well?
I'm not positive. It normally happens when i'm away from home and I get notification that my Nest cameras have gone offline. Each time it's happened, I go into the dashboard and sure enough, the AP is offline. I always attempt to ping the AP or reboot it and it's never been successful.
I would say set something up to monitor your routers connectivity. Whether it be a raspberry pi monitor, or a dynamic DNS setup so you can ping to your home from wherever you are. That will help you narrow what device to actually troubleshoot.
One thing you can do is check the firmware on both devices and make sure they are up to date.