Any conclusion about the cause of Miss Brill's loneliness is a good part inference and a small part textual evidence. There are a couple of remarks the limited third person narrator makes from which we can infer Miss Brill's past life then deduce some idea of the cause for her loneliness. Bear in mind, however, that it maybe possible that different individuals may see different inferences in the textual passages.
One of these is the remark that "Miss Brill was glad that she had decided on her fur." These fur pieces, worn as a warm decorative collar, were considered quite fashionable when newly introduced and were a mark of distinction to those women who could afford them. This may suggest that Miss Brill at one time lived in a higher level of society than that in which she presently lives, confined as she is in her "little dark room." This would further suggest a loss of fortunes, perhaps through the untimely deaths of her parents. This same sort of social fall is evidenced in an earlier story written by Austen through the character of Miss Bates in Emma. Of course, it might also be inferred that Miss Brill scrimped and saved and bought a luxury item well beyond her means, but this is less in keeping with her refined bearing, deportment and language, and therefore less likely to be the correct inference.
Other textual evidences are her red Eider down comforter, which is the most luxurious of duck down and most elegant of color of silk comforter for her time period ("Miss Brill" 1922) . Another is her refined appreciation of music and familiarity with plays. From these bits of textual evidence, it may be possible to deduce that the reason Miss Brill is lonely is that she lost her source of independent wealth, found herself in an unfamiliar lower social class and, as a result of the combination of these, remained unmarried and alone.
Nonetheless, in just defense of Miss Brill, it must be said that her pleasant smiling disposition and optimistic sunny outlook prevented her from feeling this loneliness until the heartless "hero and heroine" of the park forced the stark, cold, aging reality of her life upon her attention, bursting her dream of contentment and enjoyment of her few prized pleasures: her outings, the park band, her fur, her red Eider down, and her honeycake with its possible surprise raisin.
On her way home she usually bought a slice of honey-cake at the baker's. It was her Sunday treat. Sometimes there was an almond in her slice, sometimes not. It made a great difference. If there was an almond it was like carrying home a tiny present--a surprise--something that might very well not have been there. She hurried on the almond Sundays and struck the match for the kettle in quite a dashing way.