NEW YORK — Target shoppers found out this weekend that when stores make deals to carry merchandise from high-end designers for a limited time, it can be, well, really limiting.

The discounter partnered with the Lilly Pulitzer brand to carry a collection of 250 pieces for a fraction of the price of the Palm Beach designer’s original merchandise. But the offer, which included $38 pink shift dresses and $25 beach towels, was wrought with long lines in stores, quick sellouts online and other problems.

Cloth napkins from Target’s Lilly Pulitzer collection come in the brand’s signature colorful prints. Courtesy of Target

It shows the challenges stores face when they offer limited-time collections. They generate buzz from aspirational buyers who want to don upscale brands as well as avid wearers of the labels themselves. But the high demand can be a double-edged sword: Often, customers encounter picked-over merchandise and website snafus.

Target started selling the Lilly Pulitzer collection on Sunday online at about 4 a.m. and at stores at 8 a.m. Demand was so heavy that Target took the site offline for 20 minutes, which caused angry chatter on social media. The items sold out online within a few hours and at many of the 1,800 stores within a half hour.

Despite the issues, many experts say Target’s Lilly Pulitzer collection was a success.

“I think this was a huge success not only because Target sold out but because everyone was talking about them,” said Marshal Cohen, chief industry analyst at market researcher NPD Group.

Here are three challenges retailers face with limited-time partnerships:

DEMAND IS HARD TO PREDICT

Stores and analysts say it’s hard to gauge what shoppers will actually buy since those items haven’t ever been sold before. There was lot of buzz leading up to Target’s launch of its limited-time partnership with Neiman Marcus in 2012. Target increased production in anticipation of a sales blowout, but Target shoppers thought the line was too expensive, while well-heeled Neiman Marcus customers didn’t think it was high quality. Several weeks later, prices were slashed more than 50 percent.

SOCIAL MEDIA CAN HURT

Shoppers are increasingly turning to social media to air their complaints.

Target drummed up so much hype around its collection with upscale Italian designer Missoni in 2011 that its web site crashed and was shut down for most of the day of the launch. Shoppers voiced frustrations online and then threatened to boycott Target weeks later on social media because their online orders were being delayed and canceled.

AFTER-MARKET SELLERS

Some shoppers use these partnerships to profit by selling the stuff on eBay.

For instance, there were sold-out Lilly Pulitzer items selling for at least three times Target’s original prices on eBay. That frustrates shoppers who want to buy items just for themselves.

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