Is there any reason my mortgage payment would change over the life of my loan?
Yes. One reason may be that you have an adjustable rate loan. In this type of loan, the payments can go up or down, based on the terms of the agreement that you signed.
Some people have interest-only loans or pay option loans. With these loans, the borrower can postpone making principal payments for a while. Eventually, though, the borrower has to start paying principal and that will make the monthly payments go up.
Even if you have a fixed rate loan, your payments may change if you are paying your taxes and insurance through an escrow account maintained by your servicer. If there is a change in your property taxes, the escrow portion of your monthly payment may go up. An increase in your homeowners insurance rates also will increase your escrow payment.
If you have mortgage insurance, your payments may change once you are able to and do in fact cancel the insurance.