I think you should get it fixed, you've done an enormous amount of miles in it over the years and surely it's became a part of the family now.
I might get a quote off my local guy for the welding .. just for piece of mind .. but I'm slowly building up a list of the other things that need fixing and that worries me .. when to stop! If I strip it, that will save some money but it will probably need to be transported to the garage as it will be SORNd in a couple of weeks.
Getting rid of it now would mean getting a new car of course, a Guilia will be £25 000(?), is paying circa £24 000 more really worth it?
That said I'd also understand completely if you fancy a change, having a car for 17 years is a long time and not a lot of people would do that, that takes real dedication! - I'd also assume that you were born in 1982 (from your username), so if I'm right you must have got the car soon after passing your test - In that case you should keep it forever now but run another car as a daily or something.
Oh I wish it was my year of birth but no, that's my house number! :-) And no it wasn't my first car or last new one (counting company cars) but it was the one we kept. It was my company car for three years, and then I bought it to replace the 75. Unfortunately the job went pear-shaped soon after (think 9/11) and so it soon became my daily again.
I have been thinking about a new car .. the Giulia would be my first choice to stay in the Alfa fold, but until I can get some accurate prices, and delivery won't be until 2017 I bet (no it won't be a QV!), I'm not sure it is worth the wait .. plus then I'll be running a pretty unproven Alfa .. and we all know what that could mean! I could always come back if I stray (and we have the MiTo!)
If I had the space for the 156 and a new one maybe I'd keep it .. but the hole in the garage is reserved for something even older .. a 1958 Austin A35 that has always been on my bucket-list to restore .. that WAS my first car!! and is stored away and has less rust than the 156!!
I do have a back-up car .. but it's not the same trundling around in a 1.4 diesel Peugeot!!