Hi @whatever1980 - I'm 39 and TTC #2. Although we're considering accepting our family of three and moving on. It's a bloody hard decision!
I have very low AMH (low egg reserve) and have been told by an expert at a private clinic pretty much what you've said - it's still absolutely possible for me to get pregnant naturally.
Apparently there are lots of women walking around with low AMH who have no idea. Some get pregnant and some don't. It's all rather a lottery based on getting a 'good egg' in any given month.
He also said relaxing was very important... he says he wishes I hadn't found out about my low AMH! 
My periods are generally regular, but sometimes I have one that's a bit shorter or longer. Then I panic a bit!
This month I think I ovulated around day 19/20... so the dates are a bit delayed and hard to track. If it's coming (which it probably is), I wish my period would hurry up. Day 28 today.
I'm having my tubes tested next week (NHS) and can't be on my period at the time, so need to get it over with before then... 