Hi Anupam,
If these 2 vendors are from the same company, both of the bidders (contact persons) have been invited to participate the bidding, and you did set the flag "Allow Multiple RFx Responses for Each Company", ideally both of the contact persons could login to SRM to submit their responses. Message "A response for this RFx is already being created" might be displayed as a warning, but not an error.
If this doesn't happen in your system, I'm wondering if you have implemented BAdI, i.e. BBP_DOC_CHECK_BADI, to prevent you from creating different responses from the same company.
In addition, when you test the process, after you log off with the first bidder, please close all the IE browsers in order to make sure the session/cookies of the first bidder are cleared, and then login with the second bidder.
Hope this helps.
Regards,
Wendy