Hi there.
I have low platelets (ITP as mentioned above) - You can get low platelets just in pregnancy but mine have been low since I was 17 and I concieved with the knowledge the pregnancy (especially the birth) would be high risk. Basically you are at a higher risk of having bleeding problems - bruising, hemorraghing etc.
All the way through my pregnancy I was monitored by a haemo and my platelets were between 20 and 30. This is a normal level for me - I have been at this level for the last 10 years. Before my due date I was treated with an immunoglobulin infusion (IVIG) to try and get my platelets higher for the delivery.
If your platelets are low at delivery time (like less than 100), there will be factors to consider at delivery. You will not be allowed an epidural / spinal anasthesia. You wil not be allowed any intervention - no ventouse, forceps, fetal scalp monitoring or blood sampling etc.
The safe level for a vaginal delivery is about 50. Safe for a c-section is also 50, but a c-section carries more risk of bleeding. I was told that a section would be under general anaesthetic if I needed one (platelets had to be above 80 and stable for a spinal)
I was also induced early while the platelets were a bit better after the IVIG - before they could drop again. I did a LOT of work to try and get myself in a good position for the delivery - birth ball for positioning, raspberry leaf tea and evening priimrose oil for cervix etc. They worked - I had a 6 hr 26 min active labour, and natural delivery with just gas and air. I delivered with a platelet level of 66. You could read my birth story for more info on how things went.
One thing they did do was to give me the syntocinon drip AFTER the delivery to help my uterus contract and reduce the risk of severe bleeding. This didn't hurt - I barely noticed it.
Baby's platelets were checked after delivery and were found to be normal.
If you need any more info please PM me - I have research papers I could pass on and other people I could put you in touch with.
Good luck - it can be done and hopefully your platelets will stay high enough not to couse you any problems at all. x