DB.remove() needs to set the internal DB handle to NULL after being called.
(sourceforge pybsddb bug #737970).

Also: don't allow other threads to run during calls that invalidate the
DB handle.
diff --git a/Modules/_bsddb.c b/Modules/_bsddb.c
index eb2b516..7a4f9e1 100644
--- a/Modules/_bsddb.c
+++ b/Modules/_bsddb.c
@@ -1135,9 +1135,7 @@
     if (self->db != NULL) {
         if (self->myenvobj)
             CHECK_ENV_NOT_CLOSED(self->myenvobj);
-        MYDB_BEGIN_ALLOW_THREADS;
         err = self->db->close(self->db, flags);
-        MYDB_END_ALLOW_THREADS;
         self->db = NULL;
         RETURN_IF_ERR();
     }
@@ -1707,9 +1705,8 @@
         return NULL;
     CHECK_DB_NOT_CLOSED(self);
 
-    MYDB_BEGIN_ALLOW_THREADS;
     err = self->db->remove(self->db, filename, database, flags);
-    MYDB_END_ALLOW_THREADS;
+    self->db = NULL;
     RETURN_IF_ERR();
     RETURN_NONE();
 }