Even a Mk4 Beetle requires a 72 AmpHr [battery]...
They only put the smaller size in because there just isn't room for a larger one in a NB.
In general, a diesel requires substantial amperage to light up the glow plugs. Then on top of that, you have the difficulty of getting the high compression engine to start turning over. Throw cold oil that retards spinning and cold that reduces battery efficiency, and you have a recipe for a very large starting current requirement. And the battery has to supply that large current for more than just a few seconds. That's why you need a substantial battery for these TDIs.
You also need to drive it long enough that the alternator will be able to recharge the battery, but that's a different discussion.
The 20ma draw when idle (engine off, ECU in shutdown mode) is a good number. Your car should be able to sit for weeks like that and start easily, as in theory it would take 50 hours to consume 1 amp-hour. IN your case, I'd suspect the battery first, particularly if it starts at 12.7v then falls below 12v by the time it starts. Even if you charge it completely, a compromised battery won't hold the charge.
If the battery has been abused, such as having been completely drained multiple times, then they can start to sulfate and die on you. This is a process where the lead on the plates turns to lead sulfate and flakes off the plates. Lead always turns to lead sulfate when the battery discharges, but what is referred to is the extreme situation where the sulfate is in a sufficient thickness that it can no longer hold onto the rest of the lead in the plate. The sulfate collects at the bottom of the cell, and at that point, no matter what you do to recharge it, the plates will never come back up to their former performance level. Also, some brands are known to be weak anyway. (E.g. walmart (N)Everstart. Ask me how I know.) In the worst of these situations, the lead plates can recharge and plate lead across the plates, shorting out the cell. Obviously, this would kill the battery.
AGM (absorbent glass mat) batteries are supposedly more resistant to this type abuse, but there are huge arguments (on this forum, anyway) with no real concrete answer as to whether they can sustain operation in really cold weather (and on this forum, there probably never will be). I have a couple of them in my cars and really like them. There are several versions available, and they tend to be more expensive than comparable flood batteries. Mine happen to be made by the East Penn company, and are sold under the Duracell label at Sam's Club. This particular battery may not even be available in your area; this just happens to be what has worked and is working for me. Your results will (not 'may') vary.
Never trust a lightweight battery. The physics of the situation are that amperage requires lead and acid, and a lightweight battery can't give what it doesn't have. Period.
There are several batteries that will work, and I've made recommendations of my own. Other people will have their own pet solutions, so you'll need to see what you can get and do some research. Suffice it to say that you will need to look for a sufficient Ah rating, which is not easy to do in this country, unfortunately. Cranking amps, and cold cranking amps doesn't really tell you what you need to know since it is a mere instantaneous rating, not the one that you need after the glow cycle. Doing some research will pay off down the road.
Good luck in resolving this issue.
Cheers,
PH