Yes, Beethoven definitely suffered from a hearing loss that did grow worse over time and caused him intense physical discomfort. The earliest evidence for his hearing loss was in 1798. In an 1801 letter, Beethoven wrote to his friend and physician Franz Gerhard Wegeler that he had become weaker during the past three years. Beethoven also complained not just of hearing loss, but sharp pain, ringing, and chronic earaches. But he was not completely deaf during these early years.
So Beethoven probably could hear a number of sounds, but it was within a very limited range and got progressively worse. However, his letters also attest to the fact his hearing loss also caused a great deal of physical pain and discomfort.
There are a number of theories that have been advanced over the past century attempting to explain his deafness. There is no clear answer in that the evidence from his autopsy is quite limited and not a terribly definitive means of diagnosis given the medical science of the early nineteenth century. It's actually a pretty strong subgenre within Beethoven studies. Here are some of the leading theories:
Cochlear otosclerosis is the conventional diagnosis for his hearing loss. The onset of otosclerosis fits a general pattern for Beethoven's hearing loss; he started losing his hearing at the same age as most patients who suffer from it and the progressive nature of his hearing loss also fits. Beethoven's letters indicate that he could not hear certain types of sound typical for the onset of otosclerosis. However, there was no family history of otosclerosis and his autopsy does not display features typical of this type of hearing loss. His auditory bones have since disappeared, giving no clear answer.
Paget's Disease is another theory that uses some of the autopsy evidence. His large head and jaws, not present in the portraits of his youth, could have led to hearing loss that mimics the symptoms of otosclerosis. Paget's can also lead to deafness in some cases. However, there was little evidence supporting this diagnosis, especially the damage to the ocular nerves as the bones push on them. Beethoven may have complained of hearing loss, but there was no equivalent loss of vision.
Lead poisoning is one of the newer theories out there. Samples of Beethoven's hair indicate he had acute levels of lead in his system and there is circumstantial evidence that he imbibed lead more frequently than his contemporaries. His autopsy showed damage to his internal organs which would also fit this diagnosis. The biggest evidence against this theory is that Beethoven did not demonstrate the other symptoms of nervous system damage that typifies lead poisoning. There have been some studies from Latvia that contradict that lead poisoning results in visible nervous system damage.
Syphilis is a somewhat passe theory/diagnosis for Beethoven's hearing loss. Syphilis was a relatively common ailment in this period and not unique for a man of Beethoven's station. The two most persuasive arguments in favor of this theory are that his shrunken cochlear nerves and the fact that many of his salves and medicines allegedly used mercury (a common treatment for syphilis at the time). But the analysis of his hair by the Argonne National Laboratory indicated that there were no traces of mercury in his hair and bone samples.
In the end, these diagnoses are based upon suppositions, an autopsy done by the standards of the Romantic Era, and piecing together a diagnosis from a patchwork of letters. The simple fact is we likely will never know what definitively caused his hearing loss, but the story compels us to seek for an answer.
Sources
Lockwood, Lewis. Beethoven: The Music and the Life. New York: W.W. Norton, 2005
McCabe, Brian F. "Beethoven's deafness." Ann Otol Rhinol Laryngol 67, no. 1 (1958): 192-206.
Shearer, Patricia D. "The deafness of Beethoven: an audiologic and medical overview." Otology & Neurotology 11, no. 5 (1990): 370-374.
Stevens, Michael H., Teemarie Jacobsen, and Alicia Kay Crofts. "Lead and the deafness of Ludwig van Beethoven." The Laryngoscope 123, no. 11 (2013): 2854-2858.