Nearly certain I'm wrong, but I'll take a stab. Are you:
Pain?
I'm short
Pain is a 4-letter word
and I don't snore.
I'm not sure
I'm demanding
and can't be ignored.
Pain is a feeling sent by your nerves directly to the brain, and is basically a red flag.
When my time comes it will be inconvenience,
When you are in crippling pain, it can be difficult to walk, breathe, etc (very inconvenient).
living up to the reputation of non-lenience.
Pain is often unrelenting unless measures are taken to fix the root of the issue.
Though I am not your wife nor your girlfriend,
your saving is emptied the same way at the end.
I'm not sure
Are you thinking about love,
are you thinking about life?
Get back to work and throw your imaginary aside!
I don't really know about these as well. Pain does have the same number of letters as both love and life. Maybe the last line has something to do with fighting through the pain and that it's all in your head?
Title significance:
While people often die peacefully, death is frequently accompanied by pain. Babies come into the world crying (maybe they feel pain, I'm not sure), and childbirth is supposed to be one of the most painful events a person can endure.