Buyer asked to extend inspection period

[Joy Y.]

Hi all. I've got a deal where my tenant is under contract to buy the property I am leasing to them. This is not a lease-to-own, the lease is one agreement and the purchase is a completely separate deal. It just happens that tenant is buying. 

Anyway, the tenant has been in the property for 4 months (on a 6 month lease). At the time of contract, they originally asked for 20 day inspection period and I insisted on the standard 15. From the time they sent me the first offer until we executed was about 2 weeks of negotiating (so, this inspection period was known to be needed, and time of the essence, blah blah). We're approaching the 15 days (day after tomorrow) and they have requested tonight an extension for another 5 days. 

Is there any reason they might be using the extension to back out? Is there any reason why I might not want to grant this? I would like to sell the house, am trying to make this easy on everybody. However, if I don't sell it, the property does cash flow and I'm ok keeping it as a rental. I'm not negotiating on the price any further, nor on any concessions and I'm not paying for any repairs except I did agree that IF FHA requires repairs for the loan, I will do up to $2500. Prices are rising in my area. I haven't seen a property like mine go on the market for less than what I'm asking...in fact, most listings are 50K more than our agreed price. They are getting a good deal, and so am I. If they bail, it's ok with me. I might put it back on the market, AND she will keep paying me rent until she finds someplace else to go.

I guess I don't necessarily want to be a jerk about this, but I also don't want to be taken advantage of either. I know inspection periods are pretty important for most deals where there is competition, but I don't have other buyers, and I don't HAVE to sell this property in any urgency either. 

Thoughts? I may call my attorney tomorrow, but he'll want to be a hard ***, just because. :) I'd rather hear what the investors think.