After switching to NLB (network load balancing) server, "Upload Multiple Documents" failed on one of the web applications, but single document uploading works fine.
NLB is done through Citrix Netscaler. I cannot find anything wrong compare with other virtual servers (for other SharePoint web applications).
IIS site is created through SharePoint CA. Nothing different compare to other web application sites.
In the end, it turns out that the DNS record settings are incorrect. The record type should be "Host (A)" instead of "Alias (CNAME)".
I hope this can save you some time :-)
May need to install a Microsoft Hotfix of Office 2010.