Do the prisons have the option to block mail sent to an inmate?

The prison system never wants to get in the middle of the flow of mail from the US Postal Service. Inmate mail is considered sacred, the facility wants the inmates connected in some way to a loved one or more on the outside - postal mail is the most reliable and least expensive. They are more likely to be good inmates, quietly do their time and not come back. That is why they encourage and promote the flow of mail. Even indigent inmates are given materials and stamps at no charge to help facilitate the continuation of communication, even if they have no money to buy services.

We advise you to keep trying, this is a very tough time now for the inmate, especially when a relationship is fraying. Not answering you is the only control an inmate has. Give it some time. Just let them know you care, without being too apologetic. Keep it real. Write about stuff other than the two of you, more of a social contact and see if they finally come around.