Sale at 623 E 6th Street #5

It's a tenement building, not the rowhouse the ad claims. (Clue: on a 25'-wide building, count the windows across the width. 3=rowhouse, 4=tenement.) HDFC co-op with not one sale since they bought it from the city. The building was flooded during Sandy. More would be apparent were you to look and dig.

All leading to, they won't drop their price low enough to induce anyone to buy.

Well admittedly 1,000+ days is a lot! But it may have nothing much to do with the building or the unit at all.

There's apparently not much motivation to sell this place, for whatever reason---practical or emotional.

This can be frustrating for buyers but this is quite common, actually, and you should just move on. You might want to let the listing agent know of your interest and check in from time to time, but basically forgettaboutit.

Assuming the apartment itself is basically OK? Then my guess is that this is an estate matter. Estate matters can be complex and it's not unusual for a small apartment to be a part of an estate. Sometimes an estate matter essentially requires that the place be put up for sale, but the heirs and executor/trix are still sorting out exactly how distributions are going to work; if it sells for X amount, then it's easier to divide the assets, so they all go ahead and list it while they are all busy resolving much bigger issues.

That's in a friendly estate matter. If a will is contested, several years' delay is easy. These can last 7-10 years. The court-appointed representative can only sell real estate for a price the court and heirs permit. If that's too high, the property sits on the market while the court dates roll on.

Another scenario is when the apartment is involved somehow in the dissolution of a business entity. I met a would-be seller like this once, it was such a complex legal and angry mess it was downright scary.

Delays are more common I find with relatively inexpensive apartments with relatively low carrying costs like this one. They can make such good storage spaces that the seller is in no hurry, or the seller is going through a major life transition (e.g. taking care of an elderly parent, messy divorce, health problem, recovering from flooding, etc etc etc!) and/or is using the apartment as a guest house for visiting relatives.

Again, if you can, talk to the listing agent and see if she'll tell you what's going on.