It's a long process to quit drinking if you're a true type 1 alcoholic as described in the Big Book of AA (the type that needs to never have one drink again as we are powerless over it and can't manage our own lives whethe sober or not and we need the 12-step program to be able to live and manage our own lives). If he hasn't acknowledged he has a problem, which only he can do, then he hasn't acknowledged or contemplated what needs to come as a priority before drinking. He is still trying to quit on his own will power and that can last varying amounts of time, in this case a month or three but then the vicious cycle always starts again.
It's a horrible movie to watch someone get to bottom and first it has to get even uglier before it gets serene. If he admits he has a problem he will first have to lose most of which he puts before alcohol which sounds like currently it is his family life and your ability to rely on him to be predictable and present. I was the type of alcoholic your Dad is, whereas 1 drink was too many and 1000 was never enough. I could stop on my own will power for varying amounts of time but it never lasted. Now, finally, after decades of drinking and self medicating I am 4.5 years recovered and my Step 12 of the 12-step program is service to others who are suffering the same spiritual and physical body and mind disease.
He will have to get to his own personal rock bottom and then maybe he will admit he has a problem with alcohol. There is no point in trying to talk sense to him about it in fact that only makes an alcoholic liable to drink more or start again. It's a shitty disease that only the alcoholic can recover from without the aid of any of their loved ones. In fact especially without any aid. It's very backwards in the eyes of normal people but that's how it works.
@LevButlerov gave you a snipit into the depths to which we'll go to keep drinking. You can read my story about how far I took it to on page 2 of my log (on a desktop) or page 10 (on a device). Death from alcoholism and being brought back to life wasn't even enough for me to stop, it had to be my own personal rock bottom.