The cervix does change position during different stages of the cycle. I have never noticed any difference, but then again, I never really attempted to check it either.
"During the beginning of the cycle, the menstrual bleeding, the cervix is normally low and hard and slightly open to allow the blood flow out. It feels like the tip of your nose....After the bleeding stops the cervix remains low and hard and the o's - the opening to the uterus - remains closed. This will change the closer to ovulation you approach. The cervix rises up to the top of the vagina and becomes softer and softer. At the height of ovulation the cervix feels more like your lips than your nose and the o's are open to allow sperm to enter in. Sometimes the cervix seems to disappear - which, of course, it has simply become so soft it blends in with the vagina walls and rises so high that the finger cannot touch it. This is known as SHOW - soft, high, open and wet."
http://www.suite101.com/article.cfm/precon
ception/32502
"A combination of charting your basal body temperature (BBT), cervical mucus and cervical position and shape will indicate when the most fertile time of your cycle is. Cervical change signals general fluctuations in your estrogen levels and can be very helpful and fairly reliable in predicting your fertility."
http://www.pregnancylounge.com/cervix.php
