Is this happening on the very first instance that's created? Or only on all the rest of them?
See:
http://msdn.microsoft.com/en-us/library/47ek66wy.aspx[
^]
Which states in part:
"requests to open the file for writing by this or another process will fail until the FileStream object has been closed, but read attempts will succeed"
It looks like you are creating the filestream in the constructor, but don't close it until you use other method.
The filestream is opened for write by the very first instance that gets created. Any subsequent instances will fail because they can't get write access.
Minimally you should move the creation of the Filestream out of your contstructor and only do it just before you write to it, then immediately close it after writing to it.
But even that won't work if you get more than one request from different clients at the same time.
The easiest thing to do would be to log the log entries into your database -- the database will handle the locking / concurrency issues for you.