This notification is due to the Switch running out of RAM/memory when loading the page, and also happens on the WiiU and 3DS browsers as well.
On one hand it could be considered a limitation, but since the browser runs as an applet (it's not a full app or game) it only has access to a limited amount of memory in the first place. This is why the browser is able to work while running another game-- it's very light on resources.