I have discovered (through experimentation, since I can't find any documentation about this) that a semicolon ";" is not an allowed character in header values for uptime checks.
This is very surprising, since ";" is used in the several standard headers including Cookie, Cache-Control, Content-Type, Accept, etc.
For the Cookie header at least there is a workaround, if you provide multiple Cookie headers, they will be combined with ";", which is itself surprising because multiple Cookie headers isn't allowed, and multiple headers are usually combined with "," not ";". But this is rather unexpected, and I shoudl be able to just enter multiple cookies in the Cookie header as it would normally appear in the http header.