Your grace period stays regardless. Just continue to PIF and you won't pay interest. I used to take temporary APR reductions from them every 7 months and it never affected my grace period.
The only reason not to take these offers is if you are ABSOLUTELY sure you won't need to borrow from them at a reduced rate.
I pass on these unless the offer is 0% to tell them "try harder, not good enough."
Cap1 hands these out like candy. Every 7 months or so.