I was paying my mortgage twice a month. Can you answer my questions?

I bought a house in 2010. I found out almost a week later, my mortgage payments were going to Central Mortgage in Arkansas. I received a letter 2 days ago saying its been transferred to another mortgage company, and the new mortgage company will not accept bi weekly payments. According to the gal on the phone, they are not set up for bi weekly payments.
I was concerned, so I called and they told me I will have the last bi weekly payment taken out of my checking on 4/13, and that is the end of my business with Central Mortgage. I have to pay the entire payment on the 1st of every month starting 5/1 since the new mortgage company doesnt accept bi weekly mortgage payments.
What do you think the chances of my mortgage being “sold” to a new company again? Can the mortgage company refuse to accept bi weekly payments, and not follow thru with the arrangements I already had with Central Mortgage? Whats the deal?
I have an emergency fund. I keep a lot of money in a credit union account, and I also have a 403B.
I just like the every 2 week payments.

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