It's an implied term of your contract with the property management agent that he has the necessary skill to provide a property management service and that he will provide the service with skill, competence and diligence.
On the face of it, ignoring the issue of a leak for four days doesn't look very diligent, so there's the makings here of a breach of contract. But we don't have the full picture; we don't know why the agent did nothing for four days, or what he would say he did nothing. So while there's a good argument that there's a breach of contract here, at this point we can't say it's a slam-dunk.
If there's a breach of contract, then you can recover damages from him. So, if because of the 4-day delay the property suffered damage and has to be repaired, you can sue him for the cost of the repairs.
But not necessarily the full cost. He might argue, e.g. that the leak had been going on for some time before he was notified of it and, if he had acted as diligently as he should, it would still have been at best the following day before he could get a plumber there, and for these reasons some degree of damage - possibly quite a high degree - was inevitable. You can only recover compensation for the additional damage that wouldn't have arisen but for his want of diligence. Plenty of room for an argument about how that should be measured.
It may also be a term of your contract with him — you'll have to check this — that you will keep the property adequately insured, and that you can't pursue him for compensation in respect of a loss to the extent that you are compensated by the insurance company for that loss.
If you want to pursue this, you're looking at court proceedings - District Court or Circuit Court (or, I suppose, High Court) depending on the amount of compensation you reckon you're entitled to.
You're under a duty to mitigate your losses. In this context, that means you don't sit around letting the property decay further while you wait for him to pay you to get it fixed, or argue with him about whether he should pay you; you fix the property, and then chase him.
Of course, you also have the sanction of terminating the contract and taking your business to another agent who will (you hope) provide a better service.