In Simple mode the transaction log will automatically truncate when it gets
70% full.  That means that the space in the log file of any transactions
that are fully committed or rolled back can be reused again.  That is as
long as there are no open transactions in the way.  The log file gets used
in like a big circle.  It starts filling up the log from the beginning of
the file and when it gets to the end it wraps around to the beginning again.
If the transactions at the beginning have been committed they will get
truncated (essentially flagged so they can be overwritten) when the log
reached 70% full.  That way it can wrap around and reuse the space.  If
there is a long running open transaction in there it can not reuse the space
and will attempt to grow the log file until it can safely wrap around again.
So if the application is starting a transaction and never committing it the
log file will fill up and you will get this error.  Usually this happens
when there is an error and the app doesn't clean up after it self and issue
a rollback. Closing the connection will automatically roll back the
transactions that the connection may have had open.  I don't know how large
your db is but 350MB is not that large for a log file.  A simple reindexing
of a table close to that size can fill the log file up on it's own.  Since
you have it at a fixed size it will error when full.