This article considers a house allocation setting–where exactly one object has to be assigned to each agent–in a repeated context, where the same allocation problem is decided a fixed given number of times, while taking previous decisions into account. Since fairness can be rarely achieved in a one-shot decision, we study whether fairness over time can be reached. In particular, we use several fairness criteria adapted to this particular repeated house allocation setting and investigate whether they can be satisfied. While we show that most related decision problems are computationally hard in general, we identify restricted positive cases.