Try to take it as a compliment. From someone who has BTDT I can tell you it's more annoying and quite a bit hurtful when nobody asks to look after your baby.

I was hounded with my first and second with Grandparents offering but it doesn't happen with my younger two and TBH it would be nice if I was asked. I always feel like I'm being a PIA if I do the asking.

I totally get that you're not ready to leave your baby and don't like feeling pressured into it though