This is just a few tips from my own findings with the 156 alarm and keyfobs (flip out key type 2001 model).
When I bought my car neither remote worked but I was told that one had been working up until the day before. Once home I had a look and noticed the light flashed on one but not the other so I went and bought a new battery for it. When I put the battery in, the light stayed on constant but after a couple of presses it went out. I tried it on the car and the boot release worked but not the alarm, though that button felt different, so I took it apart. Inside I found that the microswitch had broken and needed replacing. I haven't found a source for this yet but they are similar to tv remotes and playstation controllers so if you have an old one of these it might be worth taking it apart, soldering it shouldn't be too difficult.
I then tried the new battery in the other remote but this still refused to work although the red led did flash. I tried driving with this key for a few days to see if it would re-sync to the car but it never did. I then searched these forums and found a small note stating that the red led should stay on when you first insert the battery, so i tried removing and reinserting but the light never stayed on. I then decided to take this one apart too, everything seemed fine inside so I put it back together and when I put the battery back in, the led stayed on. Tried it on my car and it all works fine now!!
So my conclusion is that if yours isn't working, replace the battery, but if the led doesn't stay on when you put the new one in, remove it again and leave it out for a while then try again until the light does stay on as this seems to reset them back to default.
If anyone isn't sure how to take one apart, flip open the key and you will see a small screw, turn this 1/4 turn to unlock the battery and then prise it out. Next you need to remove the Alfa badge, if you press down near the letter L the other end should lift enough so that you can remove it. Underneath is a small crosshead screw which you then remove before prising the whole unit apart. Be aware the the key is spring loaded and will try to flip around, just unwind the tension carefully, and wind it back up when you put it back together.
Hope this helps someone