I had the same issue.
My pencil was in a loop (attached to my iPad Pro case) but somewhere between pulling it out of my bag and going upstairs to bed, the cap disappeared. I've searched the whole house but no luck. ANYWAY...
I called support and was told they had no replacement caps but I could purchase another Apple Pencil or use my Apple Care to get one.
"HUH? WHA...?!"
As mentioned by many others, it's a weak design choice and should have been better thought out. Maybe some in-person user testing would have surfaced the issue earlier. Either way, I was not satisfied with the answer I received. I immediately went to the support site and selected the online chat option. I entered my serial number and after a decent wait for an available rep, I explained the situation. A few minutes later, I was told it'd be $8.95 +tax (and way too much for shipping) and they emailed a link to pay for the "repair" and get the new caps (for that much in shipping, might as well get two!) in the mail ASAP.
So, in conclusion...
YES, it's a poor design. I'm sure Apple will fix this with the Apple Pencil 2. Have your wallet at the ready.
YES, it's confusing. If depending on how you contact them and who you talk to, you get different answers, there's a customer support problem. Never thought I'd say that in regard to Apple, but it is what it is.
And finally YES, you can get a replacement (and possibly for free, according to a few posts on here) but you have to be persistent. Never give up, never surrender!
P.S. It sounds like buying a cozy/cap band from Amazon.com is a good idea.