You said you "keep" asking for references, wouldn't you just use the same three over and over? And if they said yes the first time, I would assume that lasts for a 3-6 month window at least, not just for the one job application it was for. You have enough steps to deal with, don't add imaginary social obligations.
You want to know the truth, I've never asked for references. I just put the person's name down and let them get a call out of the blue, on the rare occasion that the employer even follows up on them. It's not like I'm asking them to write me a letter of recommendation--if I were to ask them if I could list them as a reference, just that conversation would take up as much of their time as the surprise phone call itself. I've been put as a reference for tons of people myself, and only two have ever called. (Well, also another two for the FBI, but those were for security clearance, not a job application. And besides that, one of the FBI friends hadn't warned me I was being listed as a reference for him either.)
I'm sure now is when everyone tells me it's very rude not to ask. A pox on all your houses. I'll not abet inefficiency.