yes it is possible. urologists seem to believe that it is linked to genuine stress incontinence rather than the urge type of urinary incontinence. if the amount of loss is not large or does not seem to be urine your may be having the controversial diagnosis of "female ejaculation". apparent female ejaculation has been long debated in the medical and sex therapy literature. there is an anatomic area analogous to the male prostate which is located behind the anterior vaginal wall (ie area reputed to be the female "g spot"). this is supposed to be the source of some type of fluid which is ejected. . . given that your leakage is continuous it may well be urine. i would urge you see a urologist for a more "for sure" diagnosis. can you have intercourse if you have prolapsed bladder.
is it possible to have bladder leakage during sex? it can be continuous leakage at times.