Minis do not like to be pot bound, but they don't especially like to have too much room either. When I grew minis in 5-gallon containers, I always planted lots of annuals or tender perennials in the same container. The companion plants can absorb the excess moisture that could be harmful to the potted rose. Lobelia and petunias are nice companion plants for potted roses.
I always repotted my container roses every two or three years, even if they were going to be replanted in a container of the same size. The soil in a container quickly gets depleted of nutrients or gets compacted, neither of which provides a good growing medium.