I wouldn't say they went wrong, would just say Japanese quality and falling manufacturing costs overtook their market share in the 1980s. Even in the '70s, Daiwa was coming on strong. Today, most people buy Shimano reels.
Garcia really didn't manufacture as much as they bought manufacturers to plug into their distribution network.
For fly fishing, they got left out of the pro shop network that sprung up in the 1980s, but they also didn't offer the benchmade tackle sold in pro shops - same as Pflueger (Martin hung in there for awhile, mostly because of supplying entry level reels to Orvis).
Abu Garcia is still here - they're just all offshore manufacturing like most others.
(exceptions, St. Croix, Lamiglas - I picked two brands currenly offering US-made glass rods - though both probably make more money on the part of their business they import).
Abu Revo is the predominant low-profile baitcaster among pro bass fishermen.
http://www.abugarcia.com/yes, no fly tackle, but they're still doing what they always did, excepting of course they're not making Conolon blanks in California, Abu reels in Sweden, Mitchell reels in France, nor importing JW Young fly reels.
Conolon was a pioneer in glass rods and part of the postwar entertainment marketing boom. Mitchell quietly began the CAP reel before the war, but really took off with the postwar entertainment boom. Garcia doesn't really have a claim, other than buying the companies and moving their products to stores. Discount stores like Gibson's sold their bread and butter, and Oshman's flew their prestige flag.
Browning did something similar when they bought Silaflex to increase their market share. There were some good reels marked Browning, and Browning didn't make any of them. All through the 70s, the Browning mark raised the Silaflex image and reputation until the two words became synonymous to fishermen. And they did have some really classy product brochures. They were never sold at Gibson's, only Oshman's.
Sometime in the 80s, exactly coinciding with graphite, Sage took their place in the fly fishing food chain, while bait and spin fishing rods were taken over by a mix of Japanese (Daiwa) and US cottage industry (Falcon, e.g.). One thing that has always helped rod makers to remain domestic is the shipping cost of importing rods and blanks. Domestic rod makers also have a support advantage - warranty and customer relations.
Today and already for most of a generation, the fly fishing pro shops met their own demise, have been replaced by the giant box stores, and especially by the internet.
I know people somehow see Cabelas as having been abused by BPS, but for a generation now have been one in the same, far from their roots as marketing economy dictated - they both make more money marking up a floor full of crap than they make on fishing tackle. Orvis makes their money selling home decorations to women and prestige luggage to men - they've chosen to lose money selling fly tackle to retain their roots. Part of the reason for this is that fishing tackle fits a durable goods model - we buy a limited number of rods and reels, don't use them as often as we'd like to, fish them our whole lives and they often continue on after us, as forums like this one show.