When you have been in first for a while and yet they have not signed yet, does anyone else start nudge your offers down a little at a time?  It hasn't bitten me yet and the amounts of money I am saving aren't huge, but it seems to be working for me.

I do it. Many do. And it saves a lot of $$$. BUT, it will bit you in the *** from time to time. I had an offer in on a major FA for basically the entire FA week 2 seasons ago, without ever being in 1st place. Then, on the next-to-last cycle, the guy signed with me out of the blue. Turns out the team in 1st place had been inching down on his bid, and he inched just below my bid, and the guy signed with me right away at that point. Turned out great for me- got an All Star SP at a really freasonable price.

I've done this. I signed a very good pitcher for 8 mil this year, but originally it had started at 10.5 mil. I used the other 2.5 mil to aquire a hard hitting C

How long does it take for IFAs to sign once they become available? I know it varies but is it typically 3-4 days?, 10 cycles? What is the maximum you have seen?

If there is a pattern I haven't found it.

The one thing I have found is that if a player has been on the market for quite some time without any offers they will sign with you, a cycle or 2 after your offer. I know this from signing some junk arms to fill out the rookie squad in the past.