Not sure if the airboxes are all the same on the 156 eninges. But, I had a similar problem and I got around it by installing an Apexi filter. That was over 18 months ago and I have never looked back - works so much better than the original sloppy airbox design, and was much cheaper than a replacement box.
I was inspired by Redd and Stevo's thread (who have a pdf write-up) on this link: ItaliaAuto â€¢ View topic - Installing Apexi filter into 156 stock airbox
However mine, like yours, is a facelift so needed to do a bit more work than described in the pdf to get the Apexi filter to fit in the original box. Here is what I used:
1. Sand paper 80 and 120 grit.
2. Silicon pipe reduce 76mm > 70mm (these are internal diameters); 127mm long. I bought mine from Ramair who have a shop in ebay. I cannot quite remember if I had to trim the hose (at the small diameter end) to prevent the u-pipe doesn't fouling the bonnet (when bonnet is shut).
3. Jubilee clips.
I needed the sandpaper because the overall diameter of the Apexi filter is larger than the diameter of the box by few milimeters. So I started sanding the airbox edge with the 80grt and test fitted every few rubs. Once the filter was in, I smoothed the the 80grit scratches out with the 120....like anyone will ever see them!
The 76mm end goes onto the filter, and the other end to the air sensor housing.
My airbox cover was not completely blown-off like yours, but I don't think hot air from the engine bay will make it's way very easily there (remember the sanding bit - tight fit)...
here's a couple of photos to give you an idea....good luck