This seems a bit odd for sure. Normally if you have comments enabled, you will get a new comment form on any post with comments.
Enabling comments is usually controlled by Dashboard -> Settings -> Discussion. Did you accidentally check the box to “Automatically close comments on posts older than xx days”? Or perhaps the “Users must be registered … “?
Do you have comments enabled in the other settings? Have you recently installed any comment handling plugin?
Comment: Been a while since I’ve seen that old Wheat header image. I’d guess you’ve been using Weaver and updating for some time.