During Online bidding Ariba takes more steps towads security measure as there is real time exchange of information.
In your case the supplier's system IP Address changed significantly which Ariba does not permit. You can ask your Suppliers to change their IP setting to Static IP which will prevent this type of security warning in future.
It wise to include Surrogate Bidders in Team tab of every sourcing event and assign a user to this group. At times we may encounter this kind of error and there may be some situation we may feel that we don't want to loose supplier at any cost ,since both has spend huge amount of time.
At this crucial point of time, Sourcing Event user needs to call the supplier who has the issue and tell them that you can bid through help of (Surrogate Bidder) on behalf of them and you can get their response and you need to login as Surrogate Bidder user as shown in the snap shot below
Upon selecting supplier check box and sourcing event user needs to click on Surrogate Bid button this will take you to supplier Bid page
You can notice that you are acting as supplier and once you fill all required information you can stop acting as a supplier
Above idea would be remedy and we need to identify permanent fix as suggested by Aditya