I'm looking at possibly setting up broadband in a building only used occasionally. When not occupied, the power to the building is off. The router will be left running on battery power. Mi-fi routers are battery powered, so it's likely that on entering the building and turning on the power, the router would need to recover after running down the battery. Are there any units that will start operating quickly after such a restart? The risks seem to be: loss of settings, inability to start until battery has recharged, inability to start when the battery voltage rises slowly, requiring a manual start after recharging.
For this occasional use I'm also looking at using a pre-paid sim, so we aren't paying monthly for data we do not use, but use up credit only when needed.

Any comments please?