A closed Sears store in the weeds, with its name a faint shadow.

The drip, drip, drip of Sears Holdings Corp.'s  (SHLD)  demise keeps splattering all over the place.

Although they "missed the mark on pricing," Amazon.com Inc. (AMZN - Get Report) and Walmart Stores Inc.'s (WMT - Get Report) Jet.com expanded their appliance offerings over the July 4 holiday, BMO Capital Markets wrote in a note published on Wednesday, July 19.

While home improvement retailers, including Lowe's Cos. Inc. (LOW - Get Report) , Home Depot Inc. (HD - Get Report) , Best Buy Co. Inc. (BBY - Get Report) and even J.C. Penney Co. Inc. (JCP - Get Report)  , had better promotional deals on appliances than Amazon and Jet around the recent holiday, "when we started tracking Amazon's and Jet.com's appliances in May, we noticed emerging lower prices," BMO analysts Wayne Hood, Brian Welsh and Steve McManus wrote.

"We would become increasingly concerned if Amazon and Jet.com widened their assortment, [brought] appliances in-house instead of relying on 3P [third-party] sellers, offered free delivery and installation services, bundled offers and special buys and developed strong financing options," the three added in the note.

Even with Amazon and Jet seemingly scaling back on promotions, the fact that they are expanding their appliance offerings at all could prove damaging to Sears, which is still heavily dependent on its appliance sales and installation services—another area Amazon reportedly is trying to make headway.

When customers buy appliances on Amazon.com, they are now being "prompted to purchase installation services," according to BMO.

In an earlier research note, BMO said Sears' appliance offering dropped to 1,600 products in June from 2,002 in January.

Plus, once the leader in appliances, Sears ranked third on the 2017 TWICE Top 50 Appliance Retailers rankings with $3.8 billion in appliance sales for calendar year 2016, a 9.5% decline from the prior year. The struggling retailer was behind Lowe's, which saw its appliance sales rise 7.9% to $7.1 billion, and Home Depot, which had an 11.1% sales boost to $5.9 billion.

On July 7, Sears CEO and Chairman Eddie Lampert announced in a blog post that the retailer would be closing an additional eight Sears and 35 Kmart stores in October, on top of the 265 locations it already planned to shutter this year.

Sears spokesman Howard Riefs did not immediately return a request for comment.

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