How can a seeker of knowledge overcome the discouragement and frustration that afflicts him when he feels he will not be able to acquire knowledge?

Age is not an impediment to seeking knowledge. Many Companions embraced Islam at advanced ages, and great scholars like Ibn Hazm al-Andalusi began seeking knowledge late in life. Despair over catching up with scholars is a whisper from Satan and a weakness of the soul. What is required is diligent effort and asking Allah for His bounty, as stated in the verse: "And do not covet that by which Allah has favored some of you over others. For men is a share of what they have earned, and for women is a share of what they have earned. And ask Allah of His bounty." So, one must strive and ask Allah, abandon the whispers of Satan, and fear Allah and rely upon Him, for whoever fears Allah, He will make for him a way out and ease.