It was a number of factors.
Firstly, Commodore never really knew what they had in the Amiga and hence didn't know how to market it - it was the first affordable multimedia computer but back then no-one really understood the impact that high-resolution colour graphics would have in the future - hence it was generally dismissed as a games machine.
Secondly, they (the management) couldn't decide on a direction for the machine - initially they tried to pitch the A1000 as a business machine but when that (and moreso the A500) took off for gaming, they seemed content so long as the Amiga was selling - they never really encouraged high-quality office/creative applications on the machine which allowed the PC to quickly overtake the Amiga in business use.
That lack of direction spilled into hardware development too - the A600 was originally supposed to be a 'cost-reduced' Amiga 500 (or, the A300) - it ended up costing them as much to make as the A500 did. The AGA chipset was intended to be more than a graphics update (for the 3000+) but in an effort to reduce costs Commodore planned to release an A3200 and A3400 using ECS instead - this was scrapped because none of the regional distributors wanted another ECS machine and AGA was quickly (un)finished and bundled into the A1200 and A4000.
Commodore also dabbled in the PC marketplace for a while making their own PC clones (in fact, the A4000 desktop case was designed for their PC line) - this lost them a pile of cash they should have been investing in the Amiga. The CDTV was a huge and costly mistake too - Commodore even tried to distance it from their computers by not mentioning Amiga in the branding and advertising.
Hidden in the OS of the first A500 was a message from Jay Miner and the rest of the Amiga team:
We made Amiga, they f**ked it up - it proved more prophetic than they ever could have known...
*Edit* here's some (edited for length) quotes from Dave Haynie:
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I was working on a thing called the Amiga 3000+, which was the A3000 as you know it, with an AT&T DSP3210 coprocessor, 16-bit CD-quality audio, the Pandora (aka AA, aka AGA) chipset, and a few other things things.
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Parallel to this was a system we had dubbed the A1000+... an intermediate machine between the A500 and the A3000. A 25MHz Amiga with fast RAM for under $800, separate keyboard, CPU upgrade option, and two expansion slots... I think we could have sold millions.
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Mehdi Ali turned his sights on Engineering - he pushed Jeff Porter and Henri Rubin aside - the management team that delivered every Amiga other than the A1000, to date. He brought in Bill Sydnes who immediately set out to sabotage everything currently in the works. Politics, and stupid ones.
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There wasn't much of a way to sabotage both the A3000+ and A1000+ and still deliver them for April. So Syndes dreamed up an alternative: release stripped down versions of the A3000: no AA chips, no 68040, etc. Strip out SCSI, maybe a few other things. Still got ECS. They did a super simple gate array to lower the cost of the crazy A3000 bus buffering. This was going to be two models, a 2-slot machine dubbed the A3200, and a 4-slot machine dubbed the A3400.
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No one ordered a single unit of the A3200 or A3400. Since 1988 they had been waiting for better graphics. They needed AA... they wanted AAA. None of these machines were produced, and Sydnes' went crazy and rushed the A4000 out the door... A crippled version of what we wanted to do, but at least it was a crippled version of the A3000+ (no SCSI, no DSP, the really bad PATA bus).. and Scott's cheap '040 module.. the original A4000 motherboard didn't even have a CPU on it.
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The full interview
here 
And a wonderful
'history of the Amiga' article