'I thought the ping reply to the ISP gateway should be constant and should be 1 and 2 msec' --> Not correct.
It all depends on the traffic usage on the interface connected to ISP (provided everything else is correct with ASA & ISP).
Based on your observation- 'peak hour is some times in 2000 msec or above but during off hours, the ping reply
time is 1 and 2 msec'
It appears that there is lot of internet activity from the users. If you have a monitoring tool, check to see usage during peak hours.Or you can use 'Show inter' to get an idea by looking at the counters. Monitoring will give you better insight.
Another place to look into- how the ASA connecting to ISP gateway? Thru Media converters/ long run cables or gateway device is located in the same closet as the ASA? Media converters might cause issues as well.
Thx
MS