The protocol has no practical limit on the amount of connection attributes a client can send. The theoretical limit is governed by the 64-bit integer used to store the length of the attributes but in practice this is unlikely to be reached.

Connector/C limits the attributes to 65535 bytes after which it stops accepting them. The error it returns when this limit is exceeded is CR_INVALID_PARAMETER_NO which isn't very helpful either. The documentation for the attribute also didn't mention this limit before (I added it to the wiki).