Well, curiosity got the better of me, so I went hunting through the records at baseball-reference.com and found (what I assume to be) the game I was remembering: 8/3/89 @ Cincinnati, a 2-18 drubbing. But the other two games in that series were a 5-0 win and a 2-5 loss, so the series itself doesn't really compare.
A few other futile stretches did pop out while I was searching. 9/10-13/87 @ SD produced three losses: 7-8, 0-11, and 2-10 (and there was an off day in the middle of the series; how odd is that? not likely that it was a rainout in SD).4/5-7/96 @ SD was similarly ugly: 4-10, 4-8, and 2-17. The Marlins dealt out some punishment that year, too. 7/15-17/96 @ FLA: 5-15, 2-3, and 2-11.
And, of course, who can forget last year's Rangers series? 5/20/05: 3-7. 5/21/05: 3-18. 5/22/05: 0-2. I hope we're not about to see a repeat of that.
Looking through those scores was fun. I ran across several where I thought "oh, I remember that one!", such as the 22-inning win over the Dodgers (I was at the Dome for that one).