I found the root of the issue.
The version of stunnel shipped with Ubuntu 11.10 has the following defect :
Version 4.38, 2011.06.28, urgency: MEDIUM:
* Server-side SNI implemented (RFC 3546 section 3.1) with a new service-level option "nsi".
* "socket" option also accepts "yes" and "no" for flags.
* Nagle's algorithm is now disabled by default for improved interactivity.
* A compilation fix was added for OpenSSL version < 1.0.0.
* Signal pipe set to non-blocking mode. This bug caused hangs of stunnel features based on signals, e.g. local mode, FORK threading, or configuration file reload on Unix. Win32 platform was not affected.
I've compiled the last version 4.53 and the issue has not been reproduced.
Thanks for your help!