Do alcoholics usually go back to drinking after attempting to stop?

My father was a full fledged alcoholic(for at least 15 years) until very recently when he claimed to have stopped drinking. He seemed to keep it up for about 3 or 4 months, but today I caught him drinking again. He claims that he is no longer drinking to get drunk and is only having a glass a day. What do the statistics say? Can an alcoholic really drink 1 glass a day for the rest of their lives, or will 1 glass eventually lead to more? I personally don't believe he should be drinking at all because I've heard that abstaining completely is the only way to stop for good. I'm just so afraid he's falling right back into his old habits! Any help would be very much appreciated!