Gramochs - These are all very good responses for you. I have had some issues with different fabrics as well.
I do a Blog here on Annthegran and on May 25, I will be presenting my information and research on stabilizers which is exactly your problem. Please do check it out and add your experience and, if you try some of these methods, your new outcome.
Stabliziers are one of the most difficult to nail down for a specific answer.
Iself1 is right, you might need more than one layer of stabilizer. Your backing will be important as well. I personally use a medium cutaway for the back and a medium water soluable for the top. I use the cutaway because - well, see my blog for the reasons - The Avid Embroiderer. . . 
Pat
I hope you'll visit The Avid Embroiderer my blog for some tips and tricks from someone who enjoys sharing her discoveries.