Mark Henderson answered
Yes, Beethoven did continue to compose music after he went deaf.
At the age of 26 Beethoven had already began to lose his hearing. He suffered from tinnitus (a high pitched ringing in the ears) which made it difficult for him to hear music and make conversation. The actual cause of his deafness is still debated, although it has been attributed either to typhus or to a form of auto-immune disorder.
Beethoven had first started to complain about ringing noises in his ears in 1796 - and by 1801 he had lost almost 60% of his hearing. Despite this, he continued to compose and perform music.
Impact of hearing loss on Beethoven's life and music.
in 1811, and despite being almost completely deaf, Beethoven attempted to perform his own Piano Concerto No.5 (the Emperor). The performance was an abject failure and, although he continued to compose music, he never played in public again after this performance.
Beethoven's deafness did not have any detrimental effect on his compositions, however - because like most composers he wrote his pieces in his head before putting them on to paper. His expert musical knowledge meant that he could hear the sound of his compositions in his mind's ear, without them ever having been performed before.
Believe it or not, this is not unusual - and Mozart and Britten (both of whom were not deaf) are known to have written their compositions almost entirely in their heads. In fact Beethoven himself never considered his deafness as an obstacle to his writing, though it did affect him socially and as a performer.