Catherine Howard, Henry VIII's 5th wife was sexually experienced before marrying the king. She was also accused of having an affair with the king's groom while married to the king. She obviously had sexual relations with the king himself.
Why did she not conceive at least one time with all of her sexual activity?
Did she have a recorded pregnancy at some point during her marriage to the king?
Probably not. I'm unaware of any serious historical speculation (or more importantly evidence) along those lines.
At the time having the King's babies was essentially a queen's one and only job. This went double for King Henry, as he had already executed one previous wife essentially for not producing male heirs.
Its possible of course. While not as effective as what we have today, birth control (and abortion) methods certainly existed back then. It is true that she was never known to be pregnant. However, seeing as she died at 21 that isn't entirely strange. Moreover, we have no real evidence that she was doing that, which cannot be more simply explained by other means, so any such theory runs afoul of Occam's Razor.
Of course Hanlon's Razor would instead tell us to look for stupidity, so I suppose stupidity is one possible explanation for her behavior. However, once you play that trump card at our remove, you could explain away literally any behavior (documented or not).
Another possibility is that she was feeling the pressure to produce heirs, felt that her interaction with the king wasn't certain to do the job, and went searching for others who could ... er ... act in his stead. Sadly the historical portrayals we have for her aren't a lot of help here, as they have really been all over the map.
Most historical speculation about Henry VIII's troubles with siring heirs center on the man himself. After all, with 6 wives, he is the one constant in the equation.
At least one modern authority, historian Alison Weir, believes that Catherine Howard used birth control (her book, King Henry VIII, p. 446). What form that might be is hard to say, probably some "barrier" method such as a crude diaphragm, or maybe IUD.
This would be during her "relationship" with Francis Derehem, which she did not consider a "real" relationship, and therefore did not want to have his children. She declined to say that she was "precontracted" to marry him, even though that would have allowed Henry VIII to annul their marriage, and quite possibly saved her life.
She apparently stopped using birth control after her marriage to Henry VIII. He was an old man by that time, and engaged in few relations (at least with Catherine). She perhaps "refrained" from actual sex with Culpeper, although both of them confessed to "wanting" to have sex with the other (according to Weir). Which was "enough" of a crime by itself, to convict both of them.
