I'm aware that if a server rejects a GET request, such as in the case of a 414 error for the URI being too long, I can force it to fulfill the GET request by having the server beaten, as the Talmud in Yevamos 106a states:
גט מעושה כשר ... הא כיצד טכופין אותו עד שיאמר רוצה אני
a forced GET is valid ... How so? We beat it until it says "I'm willing!"
However, I'm not aware of any such halacha regarding a POST or PUT request. What halachic recourse do I have when a server rejects a POST or PUT request?