Are you familiar with Blossom End Rot (BER)? That nearly always happens at the blossom end (opposite the stem), but can reach deep inside the tomato. Romas are much more prone to BER than other types of tomatoes.

http://hort.uwex.edu/articles/blossom-end-rot

BER nearly always can be seen on the exterior of the fruit. If your problem is only on the inside of the fruit, it's likely something else.

I don't think you have gray wall, but you might want to look at this information:
http://www.avrdc.org/pdf/tomato/graywall.pdf
This page has very different photos:
http://www.seedquest.com/id/r/rogers/tomatodiseases.htm#GRAY_WALL

Thanks for the links. It is definitely not BER, I've seen that before and haven't had a problem this summer.

I don't think it is gray wall, as the fruits look normal on the outside. I will try and snap a photos the next time a see this problem. I am stumped!

BER can be visible ONLY on the interior.

But yes, an image will help!

Just to clarify, what I was trying to say was that if mabel wasn't seeing any BER on the outside of the fruit and was only seeing the interior problem (on, apparently, a significant number of fruit), it probably isn't BER.

Does that sound right, jean? How rare or common is the entirely-interior-BER?

I was able to confirm this is BER through the states Cooperative Extension Office. Thanks for all the advice. I've included a photo.