They are a bit rare. That's why lenders are skittish. Like Mr. K said, find someone else.
The issue with them, however, is appraisal. It's only worth what the market will bear. Which means that doing the appraisal is hard. An appraisal uses "comparable sales" to determine value. If log homes are common in your area you should be OK, but here in Ohio, there's only a handful and therefore, nothing to compare them to on the appraisal. That's why they're hard. If you build a 3200 square foot home for $340,000 and there are only 3 log home sales in a 20 mile radius of you in the last year--and they are only 1000 square foot homes that sold for $140,000--it's hard to determine the actual value of yours.
That said, as long as you aren't building the only log home for miles, you really should have no issue getting it done, but be prepared to do your homework and wait a bit longer for the loan.
There are a few springing up in the area. There's a very nice one on the golf course I play, which kind of gave me the idea when it was built 5 years ago. My design comes out to 3100 square feet plus a full basement. I haven't approached a bank to actually underwrite it, but I work with bank's as my clients, and have had conversations with a lot of bankers about them and I think several posters here have it right on the appraisal bit.