Birth control pill packs typically include a week of placebo pills, without any hormones. If you skip those pills and start the next pack immediately, you can skip your period. Whether you want to do this is up to you -- it may seem weird, but there's no reason to believe it's harmful.
As Fusion reports, some sources claim you should make sure you bleed every couple of months, but there's no particular reason for that caution. Of course you should ask your doctor about any changes you'd like to make with your medication, but don't await their reaction with suspense. Here's the spoiler:
So I decided to ask some OBGYNs, and guess what? Every single one I spoke to said there's no medically necessary reason to have a period if a woman is on hormonal birth control -- but that many women simply don't know that.
If you think about it, there are plenty of other hormonal birth control methods where you don't get a break from the hormones. Those include implants, injections and the hormonal types of IUD. Taking birth control pills (or using the hormone-releasing vaginal ring) the same way isn't a problem -- although you will go through more packs of pills or rings over time. If that's fine with you, skip away.