Online bookings for his "Dismaland" exhibition were suspended last week after the attraction's website crashed.
Many users reported issues when sales resumed earlier - prompting claims the problems were deliberate.
But a spokeswoman for Banksy insisted the rumours were untrue. Tickets have now become available on the website.
She said the attraction's website was "100% real" and had crashed under "huge demand".
Dismaland, housed in a derelict lido on Weston-super-Mare's seafront, is a dark take on theme parks with a nod to Disneyland, featuring work by more than 50 artists including Bristolian Banksy.
Among those tweeting their disappointment was Mark Ã–sten, who wrote: "On Friday, I believed 'technical difficulties'. Now, I'm reluctantly believing #Banksy is trolling those after tickets for #dismaland."
Caroline Harley tweeted: "It's easier to buy tickets to see the Beatles than tickets to go to  #Dismaland"
There were suggestions the site may be fake last week.
But the artist's spokeswoman told the BBC: "It's not true. It's 100% a real website. It crashed under the number of hits it received."
North Somerset Council, which worked with Bansky on the exhibition, has insisted the website is not a hoax.
Seafront manager Darren Fairchild said the website had crashed due to an "unprecented" number of hits, despite "huge amounts of work".
Dismaland has boosted visits to the seaside resort - one tour guide told the BBC he had not seen such crowds since the 1970s.
Among the exhibits are a distorted mermaid, a dilapidated fairy castle and a boat pond where all the boats are filled with models of migrants, as well as paintings and a beach ball hovering above upturned knives.
Banksy has denied accusations he is "trolling" members of the public - after thousands have struggled to buy tickets for his new show.