It's not so much the non-profits, but the telemarketing companies they hire to make the calls. They are using the same obnoxious techniques that were used before the Do Not Call went into effect. As you described, they hang up when an answering maching picks up. The call shows up as "toll free" or "out of area" on the Caller ID. Sometimes I'll see the number, so I know it's the same telemarketer calling over and over again.
I had one, calling on behalf of a legitimate charity, ring my phone three and four times a day, every day over a period of two weeks, anytime between 9 a.m. and 8:56 pm. I knew who it was, because the first time they called, I answered and said I was too ill to discuss the charity. After two weeks of this harassment, I answered and blew off steam at the unfortunate young lady who made that call. But they got the hint, finally, and stopped calling me. My next move was to find the name and email address of the director of the charity that hired the telemarketer and give him a piece of my mind about telemarketers, how rude and inconsiderate they are, and how, by choosing that form of soliciting for my contribution, I'll never give them another dime.