Risk of Moving out without 60 Days of notice

Hi All,

Thanks in advance for you advice, here is my situation:
I am having a condominium lease of a year ending in less than two months. I have been unable to check my mails due to my absence in the country recently and missed a mail from the landlord about the rent increase. When I recalled that the termination date is coming up and notified them, it was 2 weeks late. The landlord insists that I pay an extra month of rent because I did not give them 60 days of notice.

Is this a reasonable thing for the landlord to do? They did not ask me if I was intended to continue leasing and extend my lease at all. The reason they mailed me was because of the rent increase. My condo is located at downtown and I am sure they will have no loss with my late notice because it can be rented out to someone else very easily.

If I insist to move out at the end of my original lease. Can they sue me for not giving them 60 days of notice?

Thank you very much.