What is the best way to seek compensation from a landlord?

My friend and I moved into a new apartment in mid-August. In late August, the power started randomly going out in my bedroom and bathroom. There is overhead lighting, so I don’t have many things plugged in- just a table lamp and my laptop.

At its worst, the power goes out several times an hour. Once it happened three times in five minutes. We’ve been resetting the breaker to turn it on again. The maintenance people scheduled a visit on Labor Day, didn’t show, and then came unannounced on the following Monday. They tried again last Friday and it went from a couple times an hour to a couple times a day. Last night it happened twice, and this morning I woke up and the power was off.

(Incidentally, the power often goes off on its own when I am either sleeping or at work, so it doesn’t seem like a specific appliance is overloading the system.)

This problem predates the current building manager, who started about three weeks ago. Her answer was less than helpful- she says don’t use the lamp and have the front desk call the electrician every time we lose power.

We’re ready to escalate this to the property management company and seek some compensation. I know the general guidelines about how to do this- document everything and be polite but persistent. Other than that, I’m not sure how much this problem might be worth. I’m guessing they will make us a lowball offer, so maybe we should start by asking for the maximum allowed under our lease.

If you’ve had an issue like this in the past, what strategies have you used successfully?