One elevator fell unexpectedly – with no one inside – during a routine inspection, while another has been under renovation for two years, reducing capacity in the normally high-traffic Easter period and deterring visitors.
"It's difficult to gauge," said the tower's managing director Nicolas Lefebvre in an interview with AFP, but estimated they were seeing 20,000 tourists per day in a holiday period that normally has 25,000.
Those determined to reach the top are having to wait at least a half hour longer than usual, which on a cold and drizzly Wednesday evening did not sit well with some.
"It's too bad it wasn't better organised," said Berta Bourdon, 64, who lives in Paris and had taken her visiting nine-year-old granddaughter to the tower without knowing about the longer lines.
"I wouldn't have come if I'd known," she said. "You can do a lot of things in two hours instead of waiting in the cold."
Having already waited for 40 minutes, granddaughter Mia from Berlin passed the time munching on French fries and clambering the crowd-control barriers, while Bourdon made friends.
"I've been chatting with those behind and in front and with the little one," she said.
The two idle elevators are in the tower's west and north legs – on the side closest to the Seine river – while one on the south is reserved for customers at the tower's Jules Verne restaurant, leaving just the east.
Lefebvre expects the routine inspections on the north elevator to finish at the end of April but adds that it may remain closed for longer if inspectors find renovations are needed.
In the meantime, tourists have to contend with a queue that on Wednesday snaked the length of the square beneath the tower – or take the stairs, which one mother-daughter duo visiting from California declared "too hard".
"It's a bummer to wait, but it should be worth it," said student Ida Zirakazadeh, 15, who was in Paris for the first time.
Her mother, 44-year-old dentist Sarah Zirakazadeh, added there was nothing to do but "wait and catch a cold," as she gripped her jacket tight around her neck, adding, "I've got my shell."
Not everyone understood why some would brave the cold.
"They've got to be some kind of determined people," said Paris resident Maya Wloch, a 32-year-old assistant manager at shoe store Chaussland, who hoped to show the tower Wednesday to her visiting parents from Poland.
But upon arriving the family decided it was too cold to wait for two hours and decided to come back Thursday morning dressed in warmer clothes.
"Unfortunately we have to come back tomorrow because my husband insists on seeing the tower," said mother Ewa Wloch, 57, who planned to stay on the ground out of a fear of heights.
"I've never been that high up. Well, except by plane," said her 60-year-old electrician husband Zbigniew to explain his desire to see the tower.
According to tower spokeswoman Marthe Ozbolt, the Eiffel Tower had 7.1 million visitors in 2011 and "is one of the most visited paying monuments in the world."
The busiest period is between July 15 and August 20, but the current Easter holiday season is normally a high-traffic time as well.