Will this be able to run 24/7?
4.91 amps at 110VAC is a power of 540 watts so no-matter how long a day it shines this won't work because average power in should exceed average power out by a few percent to account for conversion losses.

Your solar panel produces only 45 watts of power.

Now maybe you mean your appliance takes 4.91 amps from a 12V dc supply - this equates to a power of 59 watts and still you have a sizable deficit. Maybe your appiance uses a 5V supply at 4.91 amps? This is a power of 24.6 watts and I can see that with a little bit of clever design (sun tracking solar panel maybe) and a decent battery to power it thru the night) that this might work.