Update: "Cancellation requests will be addressed in order of travel date to help those with the most immediate needs first," Chase said in a notice to affected travelers, noting the company was trying to minimize delays. "We know this is a challenging time, and we appreciate your patience as we work through your request." On Monday, March 16, Chase made a cancellation request form available for those cardholders who booked travel through Ultimate Rewards. If your airline, hotel or travel provider is waiving cancellation fees and your departure is more than seven days away, you can submit a cancellation request using the newly available form.

Chase's Sapphire Reserve has been named one of the best credit cards for travel by numerous experts thanks in part to its many benefits, including a $300 annual travel credit, airport lounge access and a dedicated customer support line. But this week, users took to social media to complain that Chase's customer service amid the ongoing coronavirus pandemic is resulting in long hold times spanning several hours.

Though complaints about Chase wait times seemed to dominate Twitter, cardholders were also calling out customer service at American Express, Capital One and Bank of America, all of which have online travel booking portals for their cardmembers.

Over the past weeks, the threat of coronavirus, COVID-19, has grown. As of Thursday, there are over 127,800 confirmed cases worldwide and at least 1,300 people affected in the U.S., according to data compiled by Johns Hopkins University. The World Health Organization declared a global pandemic on Wednesday, and the CDC has issued warnings that the risk of a severe coronavirus infection is higher for older Americans and those with serious chronic medical conditions, including heart and lung disease and diabetes.

The scale of the virus' spread prompted many Americans to reconsider their upcoming travel plans and try to recover some of the money they spent on hotel and airline reservations. But for those who booked through their credit card company's online travel portal, getting in touch with customer service to cancel or rebook has proved challenging.

Juan Escobar, 28, purchased flights for a weekend in Chicago using his Chase Sapphire Reserve card. He planned to celebrate St. Patrick's Day and his anniversary with his wife, he tells CNBC Make It. But because his wife is diabetic, the couple decided not to risk the roughly three-hour flight from Orlando.

After multiple calls that totaled more than nine hours on hold, Escobar says he eventually got through to Chase on Thursday using a customer service number for the company's bank division. The customer service desk reportedly told Escobar the only refund option was a travel voucher, valid for one year. "That doesn't work for us, how do we know that we can travel then?" Escobar says. "My wife is diabetic and I cannot risk her getting sick."

"It's only about $200, but it's not about the money - it's the principle," he says. "We literally have travel bans and the World Health Organization and the CDC stating that we shouldn't be traveling."

Chase tells CNBC Make It that it's working with its travel partner Expedia to build out a self-service cancellation option that will launch "very soon," according to a company spokesperson. "We are addressing individual cases and will work with customers who can't reach us right now," the spokesperson said.

American Express, Capital One and Bank of America did not immediately respond to requests for comment.

Why credit card companies are fielding booking requests

Why are so many Americans calling their credit card company instead of the airline? Issuers like Chase and American Express incentivize booking travel through their internal portals, which makes the credit card companies the travel agent of record. But that means airlines and hotels may not be able to cancel or rebook the reservation on their end, so cardholders are forced to call the credit card companies for support.

If you converted your credit card points to airline miles and then made a reservation directly with the airline, this backlog probably won't affect you. Your best bet is to contact the airline to make changes to your booking.

But for those who booked through their card issuer, even credit card experts are at a standstill about what to do. Credit card expert Matt Schulz says he was on hold for over three hours on both Tuesday and Wednesday with Chase trying to cancel a flight before being disconnected.

"Obviously this is pretty small potatoes compared to other things happening right now, but it shows that issuers and banks really need to make it easier to make these sorts of changes," Schulz tells CNBC Make It.

For Escobar, the experience has soured his view on the Chase Sapphire Reserve card. He says that he wants to cancel and find another go-to travel credit card.

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If you don't have time to wait on hold, you can download the DoNotPay app ($3 per month subscription for iPhone), which uses a chatbot to provide users with a range of services, including disputing parking tickets, getting reimbursed and skipping the line for customer service. The company has already helped thousands of customers deal with coronavirus travel issues, founder Joshua Browder tells CNBC Make It.

The app has two options for users who need to get in touch with customer service. First, DoNotPay will contact the company on your behalf so you don't have to do anything. But if you do need to speak to customer service - say to rebook a flight reservation - the app also offers a "skip waiting on hold" function where a bot calls the company, navigates the teleprompts, waits on hold, and will then forward the call to you when a customer service rep is available, Browder says.

No matter how you're contacting customer service, it's worth practicing patience in the coming days and weeks. "Ultimately, all you can do is be persistent," Schulz says. "Make phone calls. Send tweets. Send emails. And the earlier in the game you can get started, the better."

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