In real world planning problems, it might not be possible for an automated agent to satisfy all the objectives assigned to it because available resources are limited. When objectives cannot all be satisfied, classical planning returns no plan. In partial satisfaction planning, it is possible to satisfy only a subset of the objectives. To solve this kind of problems, an agent could select the objectives subset and the plan that maximizes the net benefit, i.e. the sum of satisfied objectives utilities minus the sum of the cost of actions. This approach has been experimented for deterministic planning. This paper extends partial satisfaction planning for problems with uncertainty on time. For problems under uncertainty, the best subset of objectives may not be calculated at planning time. The effective duration of actions at execution time may dynamically influence the achievable subset of objectives. Our approach introduces special actions to explicitly abort objectives. This enables control on when an objective is aborted.