Do we have to sign a fixed term lease?

Our lease expires at the end of this month. Our property manager has sent notice of a rental increase and requested that we sign a new lease about 3 months ago. My wife and I are keen to buy a property and thus don't wish to sign a new fixed term lease (with special conditions – penalties & break fees for terminating early). We explained this and are happy to pay the rent increase on a month-to-month lease. However, our property manager is unhappy with this and has sent a second notice of an additional rent increase (with only 30 days notice).

Our preference is to pay the increase but not sign a new lease. Our concern though is that the property manager may send a notice to vacate before the end of the lease. Any advice?