I have roughly the same commute as you - Zones 1-3 daily (Docklands to London Bridge), and decided very early on that I'd just fork out for an annual TC. So far I've worked out that I'm saving about £20 or so per month in doing so, plus it gives me the same free reign over the important bits of London as the monthly card, without having to worry about topping up or renewing.

In fact, the only time you need to worry about topping up is if you plan to travel out of zone. Then you'll need some PAYG balance to cover the cost of the journey that isn't covered by your travelcard. I try and leave a little bit of balance on mine for emergencies. (i.e. I get blind drunk and end up stranded somewhere in North London at 2am. It's happened before.)