Emma Thomson, who runs a jewellery company in Romford, says she is losing hundreds of pounds due to delivery issues, two weeks after Royal Mail was hit by a cyber-attack.
"It's a nightmare," she told the BBC. "It's gone on too long."
Other firms that rely on posting items overseas have also expressed frustration at the impact on their business.
Royal Mail says it is "working around the clock" to resolve the issues.
The company was the victim of a ransomware attack, which affected the computer systems it uses to despatch deliveries abroad.
Ransomware is malicious computer software that encrypts data and locks up systems. Criminals usually demand payment for releasing the data.
The problem emerged on Tuesday, 10 January. Customers were told of the problem the following day.
Royal Mail has restarted the export of parcels from a backlog, and is accepting new letters for overseas, as it tries to recover from the attack.
But it is still advising people not to send new parcels internationally for now.
Businesses are frustrated at the length of time it has gone on for.
Ms Thomson says she understands Royal Mail was the victim of a cyber-attack, but thinks the company should have got things up and running again sooner.
"You'd expect they'd have measures and precautions for this kind of thing," she says.
Around 40% of Ms Thomson's sales, from her jewellery company Gemz by Emz, usually go to Ireland and the US. She relies on Royal Mail for those deliveries.
Since the cyber-attack, she has tried to use other companies to send her products internationally, but says that is costing her around £6 more per package. "That money's coming out of my pocket."
Other items that were posted before the incident are stuck in the hub, waiting to be delivered. "They've shown no sign of movement in weeks," she says.
She estimates all of this will end up costing her a few hundred pounds per month, for as long as it continues, and comes on top of the postal strikes in the run-up to Christmas, which also had an impact in her busiest week.
Sarah Turner, owner of Little Beau Sheep in Ilkely, Yorkshire, agrees that the situation is "frustrating".
"We're relying on our customers' patience and goodwill, but that will dry up," she says.
Her company, which sells wool tumble drying balls, uses Royal Mail as it is one of the more affordable providers of international deliveries for small parcels.
She has several outstanding international orders pending that she is not able to despatch due to the cyber-attack, and says sending them via alternative means would end up costing more than the item is worth.
She thinks more communication is needed. "There's no indication how long this will go on, so we're not able to advise our customers either.
"The [overall] cost [to us] will depend how long this drags on, but it just adds to the woes of last year."
She's worried that customers who are still waiting for orders may decide to cancel them, while others may hold off making purchases.
For now, she is still accepting orders, but is having to warn customers that she is not able to send her items for now.
Michelle Ovens, founder of Small Business Britain, said the problem with Royal Mail's international delivery system was "yet another headache" for firms.
"Finding opportunities abroad, particularly through exporting, is a major way small firms can pursue growth when the UK economy is flat.
"Small businesses simply cannot afford to lose out on international opportunities, so everything must be done to resolve this as soon as possible."
'Takes time to resolve'
Despite customers' frustration, Ciaran Martin, professor at University of Oxford and former chief of the National Cyber Security Centre, told the BBC that Royal Mail was "not being unusually slow".
He said it takes time to recover from these types of incidents, and it is "very rare in ransomware attacks for things to be resolved quickly".
He pointed out that when you have attacks like this, there can be extensive damage to the network which can take a long time to repair, even if a business puts in place workarounds in the meantime.
"What people don't understand about such attacks is whether or not you pay whatever the criminal is demanding, the computer networks get battered and take a while to recover regardless."
Royal Mail apologised for the disruption.
"Our initial focus is on clearing export parcels that have already been processed and are waiting to be despatched. We continue to make good progress," a spokesperson said.
The company asks customers not to send new international parcels "until further notice".