I think 3 months. Of course there are exceptions (PP issues, NICU babies, etc.) but for a normal birth and healthy baby, I think any more than 3 months starts to show that you're not thankful for the gift.
It doesn't even have to be formal either - you could at least send an email.
Re: What IYO is the acceptable timing for baby/shower 'thank you'?
Whew! I still haven't sent out thank-yous for Andersen's gifts. I've gotten some out, but not all...
I really don't understand why thank-you notes are necessary if the recipient verbally thanks the gift giver. I'd personally much rather my friends just told me "thank you" than have them send me a note. I think thank-yous are a nice gesture, but I don't expect them...especially for gifts I give for babies' births. I know all too well how hard it is to find the time one-handed to write a stack of notes, find addresses and get them in the mail in those first few weeks. I know the parents appreciate the gifts.
For a baby shower, I think within the first few months is fine. My son was born a week after my shower, a month early, and I got them done maybe a month or so after. I wasn't one who could "nap when the baby naps" so I'd work on them when he was snoozing in his bouncer. I did a few here and there. It actually made me feel like I was accomplishing something!
I can somewhat agree that a personal/intimate, verbal TY is sufficient in some cases but I still think it's not that hard to write a little note or email to follow it up. Most people put a lot of thought into their gifts and I think they like to hear that the person receiving it recognizes their efforts.
I didn't get a written OR a verbal TY for 2 gifts that I gave a friend the middle of last year. One for the shower that I wasn't able to attend, but sent a nice gift anyway, and another for the baby along with some frozen meals. I can see that I care more about TYs that some (it's just the way I was raised) but I just don't see that it's all that hard to say something. I probably wont put that much money or effort into future gifts because of it.
Well I would like to say 1 month, but I know that my wedding thank you's took me like 4 months to get them all finished. I was totally slacking on that part.
Ideally, I think 2-3 months would be ok.