Hi neebie, how far along are you? As long as you're well and there are no complications then Pilates is encouraged all the way throughout pregnancy- with some minor adaptations to exercises like core work at certain stages. I will say however some instructors are very strict with this and say from "X"'week you can't do this or that. I always treated this as a guideline and did what I was comfortable with for as long as I was comfortable! (I'm over 36 weeks now!)
I didn't tell my Pilates instructor initially that I was pregnant as didn't want friends in the class knowing. She said I should have told her in case I became unwell but I reassured her that if I felt unwell I'd have stopped!! Needless to say I always felt grand, always listen to your body and drink lots of water. Hard in those early stages when your bladder is incapable of holding more than a teaspoonful!!
There's another thread about exercising in pregnancy too, it's really reassuring! It's called "is anyone still exercising?" And it's on pregnancy- hopefully you can find it and see that many mums to be are keeping fit and keeping well!
I stopped about 12 weeks (the pilates term was up I think), exercised pretty normally until 20 weeks and since then I do this great workout. I'm 38 weeks and I can still do it: www.youtube.com/watch?v=8M7X73qN-b0
Definitely don't give it up! It's one of the best forms of exercise to do whilst pregnant.
I am 25w now and have been doing it the whole way through. There's no need to modify anything (unless you feel unwell or tired obv) before about 16w. At that point you should start limiting the time you spend flat on your back (eg if you do bridges just do one set and then roll onto your side to recover). Eventually you stop all work in your back and the modifications continue from there. My Pilates teacher said that most of her students stop at around the 34-6w mark but that if you're feeling good there's no reason not to do it the whole way through to labour. She recommends a 8-12 week break afterwards - as much for just being able to nurture yourself as for any medical reason.
I teach Pilates and have both ante and post natal qualifications. It is important to tell the instructor just to enable them to keep an eye on you although the exercises I would advise people to stop/avoid aren't until a little later on approx 16+ weeks. I am currently 27 weeks and still doing most exercises as I know my body although have avoided ones that over use your abdominal muscles (both legs up) as this can actually put more strain on the abdominals and increase diastasis. Also lying on your front (obvious reasons) and I do start to prop my ladies (and recently me) up so not completely flat but I judge that on them and the size of bump. Otherwise I have had clients doing it until the day before the give birth and I plan to! Please message if you want further advice. I am medically trained rather than a fitness instructor so do more modified Pilates anyway.
I told my teacher at 12 weeks and she started giving me modified versions of what the rest of the class were doing from then. I carried on up until about 34 weeks as couldn't get off the sofa without help from DH by that point, let alone get up off the floor!!!
As PP have said Pilates is actively encouraged in pregnancy and so I wouldn't give it up but would let your instructor know so that they can suggest any modifications for you. I currently go to a pregnancy Pilates class and the instructor has made it clear that it is important to avoid overworking the abdominal muscles and also any exercises lying on the back. A midwife friend of mine told me recently that in her experience women who have done yoga/Pilates through pregnancy tend to cope better with labour due to the breathing techniques learned (I'm hoping this turns out to be true!)