From Susun Weed:
As the mix of hormones in your blood changes during your premenopausal years, you may notice the effects on your gastrointestinal tract both directly - estrogen is a gastrointestinal stimulant and varying levels may swing you from loose stools to dry ones - and indirectly, as the hormonal load places ever heavier demands on the liver. Hormones have a strong effect on the motility of the intestinal tract. When your levels of estrogen and progesterone change (as they do throughout menopause, during pregnancy, and before menstruation and birth), your bowel patterns change, too. Your liver is, among other things, a recycling center. It breaks down hormones circulating in the blood when they are no longer needed and makes their "parts" available for the production of more hormones. During the menopausal years some hormones (such as LH and FSH) are produced in such enormous quantities that your liver may struggle to keep up with its recycling work, and have little energy left over for digestive duties. Help yourself with these Wise Woman Ways.

Your esophagus is supposed to propel food in one direction--mouth to stomach. There must be something abnormal about your esophageal motility as it is easily transporting air in the other direction. And your disordered esophageal motion must somehow be related to hormones. Research suggests that the hormonal fluctuations of a normal menstrual cycle affect how well the esophagus keeps acid (and presumably air) from burbling upwards from the stomach. Women who volunteered to swallow tubes that measure acidity and pressure (and what were they thinking?) were found to be much more likely to have stomach acid up high into their esophagi in the week or two before their periods. 

A 2008 study of perimenopausal and menopausal women done by questionnaire (older women apparently didn't fall for this tube down the esophagus sort of thing) showed that 80% of them suffered from upper intestinal discomfort, again suggesting a link between hormones (this time perhaps falling hormones) and motility problems. Of note, weight is very much related to esophageal reflux, and women our age are more likely to carry extra weight.

So there are known links between the normal or abnormal functioning of the esophagus and hormones. That said, in order to belch, you've also got to have air in the stomach, a place not normally known for much air. Women with hiatal hernias (where the part of the stomach is pulled above the diaphragm) are known to have a problem with air trapping. Some people tend to swallow air when they talk or eat. Perhaps a spastic esophagus sucks down air of its own accord.

Medication to decrease acid such as Zantac or Prilosec may decrease irritation to the esophagus and cause it to function better. Depo Provera shuts off normal cycling, so any hormonal effect on the esophagus would be decreased. Reglan (metaclopramide) promotes normal emptying of the stomach southward instead of north to the mouth. Not chewing gum, eating hard candy, or talking while eating would decrease air swallowing.
FROM DR. JUDITH PALEY ON THE MINNIE PAUZ MESSAGE BOARD (You must register first)