Can the flight price change between the search results and the payment page on my portal?

Yes, it can, and this is normal in flight booking rather than a fault with your portal. The prices your customer sees in a search come from fares the supplier has stored or cached so that results come back quickly. The real, bookable price is only confirmed at the moment the booking is being made and the airline is asked directly. In between those two moments the airline can sell the cheaper seats to someone else, reprice the fare, or update the taxes.

How often this happens depends on the airline and the supplier you are connected to. On busy routes, and with budget airlines where seats move quickly and fares are priced live, a change between search and payment is more common. On quieter routes a fare can stay the same all day. It also happens more when a customer takes a long time between searching and paying, or comes back the next morning to a search result they left open.

Most flight booking APIs have a step that checks the fare again just before payment, and a well built portal uses it. Your customer is shown the new price and asked to agree before any money is taken, so nobody is charged more than they have accepted. Whether the older price can still be honoured is not something the portal can decide, because the seat and the fare belong to the airline.

Ask your supplier how long their fares stay valid, and check that your portal is set to show the customer the new price and ask them to confirm, rather than failing the booking quietly.