Hi Bruno,
Your best would be to add one of these to your route script:
http://www.kamailio.org/dokuwiki/doku.php/core-cookbook:1.5.x#error_route
It would allow you to log the precise nature of the syntax errors in the malformed SIP messages you are receiving and to further isolate the problem from there.
Please note that this feature no longer exists in Kamailio/sip-router >= 3.0, and is superseded by the sanity_check() routine. However, it does work in 1.5.x.
Cheers,