It's a beautiful plant. I would water it more often. When I worked in a nursery in Vero Beach, Florida the owner had one at the top of a waterfall. It was under water all of the time.

10 - 12 days is too much time to go without watering a peace lily. I water mine every 7 days (it looks like the same size as yours).

You only need to water it when the leaves start to wilt.
A 10 inch pot can probably stay wet for more than 1 week.
Too much watering can cause the leaf tips to die.

When the leaves look droopy give it a good drink and the leaves will go back erect and perk up within a few hours.

DO NOT overwater it!

Even after watering the tips of the leaves stay curled. Could there be any other reason?

Maybe a build up of fertilizer or too much sun,
I have one that is kind of curled under like that but it is the natural form. My cultivar is a little different from yours.
But i think the plant looks to be in overall good shape.
Go ahead and cut off any dead flower spikes.

You might also want to look for spider mites.

Maybe try watering it with distilled water to see if that helps

I examined for Spider Mites and couldn't find any evidence.
A few leaves do have some holes in them.

I have been leaving my water out for at least 24 hours but I guess I could try to water with distilled water.

Could repotting into a different soil mix help?

Peace lilies are somewhat finicky about their moisture needs. They don't like to be to dry but will suffer if they have to much water. Experiment and see how it responds. I have had very good success with heavily misting everyday. This will help with brown tips.