...and the answer is, from Bruce's comment on his original answer: "@Breck: there is currently no mechanism for automatically recompiling events. You can, of course, put the logic for the event in a procedure which the event calls. – Bruce Hay"

Here's the scenario in 11.0.1.2276: An updated stored procedure event failed at runtime with "column not found" because of a FOR loop which referred to the new name of a column in an existing table when, in fact, the table still had the old column name. An ALTER TABLE was run to fix the column name, and the stored procedure event was re-executed, only to fail with "Invalid statement" (see below). The stored procedure event was recompiled and that got rid of the "Invalid statement" error.

If this is expected behavior, the Help should be updated to mention the possibility that a stored procedure an event should be recompiled:

http://dcx.sybase.com/index.html#1101en/saerrors_en11/errm130.html

Invalid statement 
Error constant SQLE_INVALID_STATEMENT 
ODBC 2 State ERROR 
ODBC 3 State ERROR 
Severity 16 
SQLCODE –130 
SQLSTATE 07W02 
Sybase error code 13628

Probable cause 
The statement identifier generated by a PREPARE passed to the database 
for a further operation is invalid.