Can a credit card company increase the rate if there's outstanding balance on a card?

The CARD Act prevents the credit card companies to raise interest rates on existing balances; they can only do it for future charges. So, talk to your CC company and clarify.

If you feel they have increased, then they have increased.
It's their card, their money, their interest rate... you only borrowed it!~ But you can complain why they didn't inform you!!!

But here's something I want to quote from a good website I googled:

"In most cases, the Card Act prevents credit card companies from raising the interest rate on an existing balance. In other words, if your rate goes up, the new rate will apply only to new charges going forward. "

Have you missed 2 consecutive credit card payments?

I think you got a penalty change from the credit card company. Ask them.

Even if the CC company increases the rate, i think there's a rule that they have to inform you. Check out the statements whether there's any penalty charges.

I would rather suggest you to ask your credit card company about this issue first.