Question: Is there any way to include captcha on the site and at the same time prevent services like 2captcha from resolving it?

Answer:   One can’t at this time. The captcha developers provide for humans to solve their puzzles (JS-driven, image puzzles, drag-&-drop, etc.) and services like 2captcha are also utilizing humans to solve cloned/copied captchas.

Additional thoughts

I think, however, one may strengthen protection against automated solving services. For this you impose multiple (2-3) captchas on the same web page. It’s similar to setting multiple security systems for a car. The fraudsters’ solution time will increase, and they might drop hacking your webpages.

(If you are a developer) The best that captcha developers can do in this case is to make captcha to be non-transferable, that is to develop a captcha so that such solving services can’t reproduce it (or an essential part of it) to their solvers. This is mainly applicable to JS captchas, since scripts can copy images easy.