Regarding the sacrament of Anointing of the Sick:
Is there a limit to the number of times a person can be anointed when suffering from the same illness, specifically when one has a terminal illness? For example, if a person is dianosed with cancer and is anointed when first starting chemo therapy then after a couple of years of being in and out of chemo and comes to a point of being considered “failing” can that person be anointed again? Or is this at the descretion of the person’s priest?
1515 If a sick person who received this anointing recovers his health, he can in the case of another grave illness receive this sacrament again. If during the same illness the person’s condition becomes more serious, the sacrament may be repeated. It is fitting to receive the Anointing of the Sick just prior to a serious operation. The same holds for the elderly whose frailty becomes more pronounced.
Can. 1004 §2. This sacrament can be repeated if the sick person, having recovered, again becomes gravely ill or if the condition becomes more grave during the same illness.
Anytime an ill individual’s condition can reasonably said to have become worse the person can be anointed again. There is, of course, no definitive line that we can say has been crossed it is a matter of prudential judgment. Based on your description it would be entirely appropriate to anoint such a person again.