Can we count successes and failures?
R300 - success
R420&480 - so-so
R520 - failure
R580 - failure (too late to the market)
R600 - coming late.
R580 not was a failure.
I think ATi problems started in the r420->r480 refresh timeframe, they have no sm3.0+HDR support (NV PR was very good here and many users eat the sm3.0+hdr PR, reviewers overhyped sm3.0+HDR too), NV skip the NV40 part refresh and catch up some time here what they loose with the nv3x time, than ATi loose some time with the R520, but catch back with R580, but they PR was still crap, they can't make positve things for the G7x texture shimmering, still many reviwers using default quality in G7x reviews, and some big site find this problem 2-4 weeks before G80 released. (shimmering problems exist for like 16 months).
Well, im not sure the R600 late when not arriving in Q1 because all dx10 game delayed (looks like now the first one coming early Q2), most users playing at 1280x1024 they can buy a fast DX9 ATi card. (i just noticed the x1950xtx price just droped 20% here in europe, 80-90 euro cheaper than the 8800GTS, this can mean 2 thing, first: something coming soon, second: r600 delayed and now ATi only with cheaper prices can battle with the 8800 series.
The bad thing for AMD now, when R600 delayed this means mainstream/performance cards coming later too, i think NV coming out with the g80 refresh in late Q1 or early Q2 (maybe when R600 delayed they not coming out in this timeframe with the refresh), and with the mainstream/performance cards in the same timerange, so AMD have no dx10 cards for this timeframe.
Latest numbers
http://www.xbitlabs.com/news/video/display/20061229150853.html show enthusiast market only 4% (250$-700$), if AMD have problems with the R600 why not relesing the mainstream/performance cards first? i know enthusiast market is good for PR, but 150$-249$ segment is 75%, i know no dx10 coming soon but the x1950pro will be not enough vs the G80 mainstream part because x1950pro lack of DX10 support, NV overhype PR is very good.