Keothavong also lost to Mayr at Wimbledon last year
Great Britain's Fed Cup team had their promotion hopes all-but ended as Austria clinched a comfortable 3-0 win in their Group D tie in Portugal.
Anne Keothavong's first match after six months out with a knee injury ended in a 6-2 6-2 defeat by Patricia Mayr.
And British number one Elena Baltacha lost 6-3 6-3 to world number 50 Sybille Bammer in the second singles match.
That left the doubles as a dead rubber, with Mayr and Yvonne Meusburger beating Keothavong and Sarah Borwell 6-4 6-4.
British captain Nigel Sears said: "Naturally I'm disappointed but we were beaten by a better team on the day.
"It was a lot to ask from Annie. I took a risk putting her in after being out for a long time, but she had been playing so well in practice I thought it was worth the risk and I knew that to get through perhaps the later stages of this group she would need to have some matches behind her.
"Unfortunately she couldn't come up with it today, although Mayr played very well. It was a risk I took that didn't come off.
"It's a reflection of the strength of the Austrian team that they've won both singles against Belarus and us. I think the girls gave it their very best."
The GB team, who won their opening group match against Bosnia on Wednesday, complete their campaign against Belarus on Friday.
But Austria, who are top of the group after two wins, are almost certain to progress even if they lose to Bosnia in their final tie.
Each of the four group winners in Portugal will go through to Saturday's play-off. April's World Group II play-offs await the two winning teams.