Consumers seem to like getting deals via email—right up to the point when they get sick of them and tell e-retailers to cut it out, according to data from email management system provider Sailthru Inc.

From Nov. 21-28 the total number of online purchases made via email was 60% higher and total revenue 115% higher, compared with the average of the previous 30 days, Sailthru finds. During that period, Black Friday and Cyber Monday were the highest sales days. Revenue on Black Friday was 310% higher than the average of the 30 days prior to Cyber Week, while revenue on Cyber Monday was 253% higher than average those 30 days, according to Sailthru’s data.

But, Sailthru’s data also shows that consumers hit the “unsubscribe” link in email most heavily over the days leading up to Cyber Monday, and that activity peaked on the Tuesday after Thanksgiving,  says Eric Porres chief marketing officer at Sailthru. E-retailers risk losing longer-term customers if they send too many emails during the holidays, he says.

“This suggests that consumers grow tired of the constant barrage of offers and are willing to sever brand relationships after the hype settles down,” Porres says.

Other research finds that e-retailers used email marketing to push slightly more promotions during Thanksgiving week in 2016 than in 2015, according to marketing vendor MailCharts.

MailCharts says 62% of emails sent on Black Friday 2016 contained a promotion, compared with 59% for Black Friday 2015. For Cyber Monday 2016, 62% of emails contained a promotion versus 56% in 2015.

The vast majority of those promotions were “percent off” sales (73% on Black Friday and 74% on Cyber Monday) or “dollars off” sales (21% on Black Friday and 18% on Cyber Monday). Other promotions included free shipping (4% on Black Friday and 6% on Cyber Monday) and “buy-one-get-one” (2% for both Black Friday and Cyber Monday), according to MailCharts.

Other findings:

• The average discount for Black Friday was 38%, while the average discount for Cyber Monday was 36%.
• On Black Friday, 50% off was the most popular discount, followed by 20% off and then 25% off.
• On Cyber Monday 20% was the most popular discount, followed by 50% and then 30%.

If your inbox was deluged with messages on Black Friday and Cyber Monday, you were not alone. Digital marketing vendor eDataSource, which gathers email marketing data from a panel of about 1.4 million consumers around the globe, finds that retailers sent 12,606 email campaigns on Black Friday, 55.4% more than they sent in 2015, and they sent 10,334 email campaigns on Cyber Monday, a 42.0% jump from a year earlier.

The surge in emailing happens for a good reason. It works. Adobe Digital Insights says email drove 18.1% of online sales from Nov. 1-28, behind search (38.5%) and direct traffic (25.3%), and ahead of referral sites (16.0%), display (1.2%) and social media (0.9%).

Carl Sednaoui, director of marketing for MailCharts says he is struck by how little the schedule for Black Friday and Cyber Monday email campaigns has changed year over year. He recommends retailers start communicating to their subscribers earlier. Otherwise, he says, their messages could get overlooked when inboxes fill up.

The next chance to do that, Sednaoui says, is the period between now and Free Shipping Day, Dec. 16.

According to MailCharts, 28% of emails related to Black Friday were sent on that day (nearly unchanged from 29% a year earlier), while 72% of Cyber Monday  emails were sent on that day (compared with 70% in 2015). 50% of Black Friday emails were sent from Nov. 18-24 and 23% were sent during the three days after Black Friday to promote extended or continuing sales. For Cyber Monday emails the remaining 28% were sent from Nov. 21-27.

On average, MailCharts finds, subscribers received 50% more emails on Black Friday versus the previous Friday and 68% more emails on Cyber Monday versus the previous Monday.

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