Well, ok...

From a civilian perspective: 30 days, you say!? Wow! That's totally great and impressive! Awesome!

BUT... from a military perspective... A perspective of someone familiar with energy requirements of deep space probes...

That's kinda laughable! That sucks! 30 days!?

Come on! You can do W A Y - W A Y - B E T T E R than that!

And so yes, you can: We're talking like 50 YEARS, plus or minus, of operational ability!

If you simply use the technology that the 2 latest NASA Mars Rovers use:

RTG (Radioisotope Thermoelectric Generator).

What this means is:

No need for something as complex as a reduced-size nuclear power plant. (Although the US-Navy can currently do that if they really want to!)

Instead, just operate off decades worth of thermal power, from a single small nuclear power source... emitting radiation locally that you can constantly just keep turning into powerful thermal energy induced abilities. For DECADES!

And sure...

What happens if the autonomous RTG powered ship gets sunk... then... Well...

It's admittedly not a great thing that a ship with nuclear material gets shot and sunk ("You sunk my battleship!"), and then exposed to the open ocean, but it's still pretty pretty insignificant in the grand scheme of things!

In most cases it will just sink to the bottom of deep waters, where it will be mostly inconsequential...

But even then, hey, if that still alarms you, then fair enough:

The US Navy could easily still retrieve it, and isolate it!