Connie, whether this is the case with this plant or not I can't say for certain as I have never grown it. However I do have Epi. ciliare (at least that is what I was told it was) which has flowers and buds that look quite similar to yours so maybe this will apply.
I have noticed with many of my catts and my Enc. michoacana /michuacana that the buds often develop sticky, sugary droplets at the tip of the bud and at the base of the bud. Not surprisingly this can get a bit smeared if I'm not paying attention to what I'm doing and can make for a sticky bud overall and a sticky mess on me as well. But like I said, I'm used to this with my catts & enc.
So I would not have been the least bit surprised if this had also been the case with my Epi. ciliare as there does seem to be a relatively close relationship there. However, much to my surprise, instead of the soft, sugary, tacky dewdrops I was expecting, this Epi seems to produce a substance that I would best describe as starchy. This substance coats the entire bud and does not appear as droplets. It is dry to the touch unless your fingers are slightly damp in which case if you were to hold the bud with your fingertips for a few seconds you might find your fingers sticking to the bud slightly -- again as though you had touched a dry, starchy film. With this in mind, when the first bud seemed to have difficulty opening the thought occurred to me that perhaps the starchy film was the culprit. So I took the plant over to the sink and ran some lukewarm water over each bud while gently rubbing my fingers over each but in hopes of washing this substance off. Interestingly, to me at least, was the slick -- almost soapy feel -- the buds had while I did so. Again, very much the type of sensation I would have expected of something covered with a film of starch when wet. That first bud's petals finished separating from each other as I did so -- which of course could have just resulted from the pressure of my fingers -- but the other two buds did open without any problem or need for "retreatment". I imagine if I was growing this plant in a greenhouse wherein the plant would have gotten 'rinsed' with a hose while watering, or if outside during a series of rains which would accomplish the same thing that the flowers would have opened just fine without my intervention.
Perhaps, assuming your Epi is in similar straits, a little rinse would help with yours.