I'm going to answer based on the manga, because I still have not seen the Brotherhood anime. I think this is just fine, as it seems that the anime streamlined the ending a bit.
This is going to be spoilerific, but scarcely more than the question itself, so I'm not putting all of it in spoiler tags.
Let's start at the core of the issue. You say that Father "absorbed" God. This may be a bit of a misnomer. It's more accurate to say that he simply contained God within himself to control its power. And this is the crux of his defeat.
While not explicitly stated, it's obvious that Father needs tremendous amount of energy to contain God. He already had the power of half the people of Xerxes, but his plan was to bolster this power by the souls of all the people of Amestris. However, Hohenheim managed to thwart this part of the plan by forcing the release of these souls right after they were taken.
This weakened Father's grip on God, but not enough for full release yet, although his control over his powers obviously weakened (See chapter 105, pages 32-33). After this, everybody started attacking him. The military, the rebels, Edward, May, and even blinded Roy Mustang. Father deflected all these attacks without even lifting a finger, sometimes even retaliated. However, even though he seemed to be unaffected by all these attacks, they do require energy from him to block. Slowly but surely, his energy reserves diminished to the point that he started to take damage.
This led to even more energy drainage, because now he had to use the energy to rebuild himself. Energy that he desperately needed to contain God. As the battle waged on, it became more and more obvious that God was actively battling against Father to escape. He tried to salvage the situation by absorbing Greed, but this turned against him, because Greed (and as far as I understand, only Greed) betrayed him and caused his limbs to turn fragile. That and the final punches from Edward pushed his energy reserves over the limit, and he no longer had the power to contain God. What happened next is sort of hard to explain, so I'll just refer to Chapter 108, page 21.
After all this, Father, now reduced to Dwarf in the Bottle, found himself in front of The Gate. He had a brief encounter with Truth and was then violently dragged within The Gate, to whatever fate awaited him in there.