I am wondering this as well...usually in the See Details sections on the Plans page it has a date but just says Limited Time Offer.
I have a related question seeing as I am considering switching to this plan as well. I am currently in a 2 year agreement with a $25 grandfathered plan with a monthly recurring credit of $5 on my account (I took a monthly discount instead of a new phone). If I switch to the new $39 plan, will I lose my monthly credit?
The current double your minutes offer with Standard Plans came out the same time as the $39 Smart plan ends April 30, 2013. I'm willing to bet the $39 Smart plan expires April 30 as well. Just an observation.