Objection 1. It would seem that this sacrament ought not to be repeated during the same sickness. For one disease demands one remedy. Now this sacrament is a spiritual remedy. Therefore it ought not to be repeated for one sickness.
Objection 2. Further, if a sick man could be anointed more than once during one disease, this might be done for a whole day: which is absurd.
On the contrary, Sometimes a disease lasts long after the sacrament has been received, so that the remnants of sin, against which chiefly this sacrament is given, would be contracted. Therefore it ought to be given again.
I answer that, This sacrament regards not only the sickness, but also the state of the sick man, because it ought not to be given except to those sick people who seem, in man's estimation, to be nigh to death. Now some diseases do not last long; so that if this sacrament is given at the time that the sick man is in a state of danger of death, he does not leave that state except the disease be cured, and thus he needs not to be anointed again. But if he has a relapse, it will be a second sickness, and he can be anointed again. on the other hand some diseases are of long duration, as hectic fever, dropsy and the like, and those who lie sick of them should not be anointed until they seem to be in danger of death. And if the sick man escape that danger while the disease continues, and be brought again thereby to the same state of danger, he can be anointed again, because it is, as it were, another state of sickness, although strictly speaking, it is not another sickness.
This suffices for the Replies to the Objections.
Source: Summa Theologica (New Advent)