1. I am sorry to have keep you waiting.
2. I am sorry to keep you waiting.

I know what no 1 means. It means "I am sorry that I've keep you waiting".
yes.. I can understand no1.

My problem is No2. Does it mean "I am sorry that I keep you waiting"?
From No2, It sound like to me "The speaker always not temporarily makes the listener wait", so no2 sounds a little strange to me.

However, I guess these comments are appropriate in a business circumstance when somebody arrived later than his/her partner.

I think ,therefore, both are appropriate for a temporary situation, but No2 doesn't sound so to me.
Am I thinking correctly? I need your explanation. Thanks for reading.
1. I am sorry to have kept you waiting.-- Before or up to now
2. I am sorry to keep you waiting.-- Up to now or into the future.

I'm sorry to have kept you waiting - you are no longer waiting.

I'm sorry to keep you waiting - you are still waiting.
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Icadia, I've just deleted an anony post of yours with the same question. Please, don't post duplicates anymore. Thanks! Emotion: wink
Hi there Emotion: smile the Difference between the two areTIME.

1." I'm Sorry to Keep you Waiting.."
- The Person Speaking still makes the Other Person WAIT (Continously).

2. "I'm Sorry to Have Kept You Waiting.."
- The Person Made the Other Person Wait but now the wait is OVER (Finished).

I Hope This Helps Emotion: smile