The Basic Principle is that the State of Purity remains Valid

Question :

If a person performs ablution, then some time passes, then the time for prayer arrives, and he does not remember whether he is still in a state of purity, or if he needs to make Wudhu' again, upon what should he base his judgement?

Answer:

If a person makes a complete Wudhu', remaining in a state of purity even though time has passed; then if he is in doubt as to whether his Wudhu' has been invalidated he should not pay any attention to this doubt. Rather, he should base his judgement upon what he is sure of, and that is the state of purity. This is because it has been authentically reported in the the Two Sahihs from 'Abdullah bin Zaid, may Allah be pleased with him, that a man complained to the Prophet of suspicion that he emitted something during prayer, so he said:
He should not leave unless he hears a sound or smells an odor.Al-Bukhari no. 177 and Muslim no. 361.

Based upon this, (we may say that) if some time has passed since his Wudhu', and he is in doubt over whether he is still in a state of ritual purity or not, he should pray, and there is no harm for him in that, because the basic principle is that he remains in a state of purity.

Source:
Ibn 'Uthaimin
Fatawa Islamiyah, Vol. 2 Pages 86-87