There are now loads of coolers on the market designed for summer road trips that typically plug into 12V (car) but often have available AC adapters.
These are great if you are using an ice chest for your chill water source and you want your ice blocks/ frozen soda bottles to last longer.
This is not a plug for Igloo - there are MANY, just an example of what is out there
We have NOT DONE ANY DIRECT TESTING OURSELVES, just anecdotal indications from customers mails, etc. Please note we are not endorsing a particular brand or even that these work. But based on a few customer mails and the specs / descriptions of these types of coolers there is no reason to think they couldn't sustain your ice longer than not having any cooling at all.