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Regarding your post, I can certainly look into this for you. I'll follow up with more information.
Typically the points buyback offer is only good until the end of April. After that the only way to regain status is through stays (or by completing a challenge).
To get back to Gold for a basic level, earn 10 nights (though stays or a Marriott Rewards credit card) to reach Silver. Then either complete a Gold challenge or reach 50 nights.
I don't think there is much rhyme or reason as to when Marriott will offer a Gold challenge. Sometimes if it looks like I guest will achieve Gold status in the coming year, the challenge might be offered in hopes of increased spending to try to get to (or retain the temporary) Gold status earlier than might otherwise happen.
As for requesting a challenge, most Silver members find that calling the customer service line is all it takes to get signed up. It does take 6 separate stays over a 3 month period to reach Gold, so it's better to call when you know you will have some upcoming travel. I've also heard that if you call during the last half of the month, you could have the remainder of that month plus the regular 3 months to complete the required stays, though I can't confirm this from experience.
I was offered a Gold challenge twice while at the Silver level. The first time, I wasn't able to complete it, but had the temporary status for a few months. The second time, I reached 50 nights a few days before the challenge began and called to get switched to a Platinum challenge. In any case, only one challenge is allowed per year. One benefit is that the new status continues until February two years hence (so if you complete a Gold challenge in 2015, you'll stay Gold until Feb 2017 (even if you don't end the year with the required 50 nights).