I have my website similar to pastebin. There is a text box on the index.php and a captcha code to complete after you finish typing to upload the paste. If you enter the wrong code, as many do, including me, a new page comes up that says you mistyped, then when you go back to index.php then everything you have written in the text box gone? Isn’t cookies or cache that can save this?
I agree that only the captcha should be empty while returning to the same page and the rest of the form, whatever it is, should be remain filled.
Javascript could do the job much easier and should solve the problem for this, though if you want a javascript free page (that is, that even works with perfectly with JS turned off) you may want to use cookies instead
Show us the code you have to draw the form, and to process the input, and someone will show you where it needs to be edited. Basically where your error-checking happens, you need to either stick the text you want to keep into a cookie so that the form can retrieve it to populate the text box value field, or generate the form from your php code and output it from there.