In 5e, what does the spell do?
You hide a chest, and all its contents, on the Ethereal Plane...While the chest remains on the Ethereal Plane, you can use an action and touch the replica to recall the chest...If the spell ends and the larger chest is on the Ethereal Plane, it is irretrievably lost.
We know that one of the spell effects is that it "hides" the chest - so what does it mean to be hidden? In 5e, can hidden things be found?
Well, yes, if they are game-term Hidden. To find something game-term Hidden, you just need a Perception (roll or passive score) better than the Stealth (roll or DC) of the thing that is Hidden. But the spell doesn't seem like it is using Hidden in this sense, so it is likely using hidden in the plain English sense. In natural English, can hidden things be found? Why, yes again - so it might be possible to find chests that were hidden by the spell.
In natural English it is not clear, however, whether the action of the spell hides the chest as a 'one and done' event ('I hid the cookies in the cupboard'), or continually hides the chest throughout the duration of the spell ('The clouds hid the moon all night'). If the chest is hidden the first way, it most certainly could be found, but if it is hidden the second way, it might not be possible to find it without somehow ending or overcoming the spell.
The spell does not only hide the chest, though - it also can be used to recall the chest from its hiding place. This is important because if the chest is still hidden when the spell ends, it is "irretrievably lost". In natural English, something that is irretrievably lost can't be retrieved, but might still be found. It is a spell effect that recalls the chest from the Ethereal, and once the spell ends, it can no longer do that, but this doesn't preclude other means of recovering the chest. As a linguistic analogy, suppose the chest is a lure and the spell is a fishing line. When I go deep sea fishing, every time I cast, I can retrieve my lure. But if my line breaks, my lure is irretrievably lost, because I can no longer retrieve it. It is not completely lost, though, as I could go diving and attempt to find the lost lure on the sea floor. It is lost, but it could be found.
So, my best RAW analysis says that chests that were hidden by the spell can be found on the Ethereal, but they are no longer accessible from the Prime - you would need to go the Ethereal itself and look for them - much as the hags from Icewind Dale do, as Thomas Markov's answer relates. It remains unclear whether the chests there were just hidden once or are 'actively' hidden while the spell is still running; that is, it is unclear whether or not the only chests that can be found are those on which the spell has ended.
In previous editions, the chest could be found while hidden
From the First Edition Leomund's Secret Chest spell description:
While on the ethereal plane, there is a 1% cumulative chance per week that some creature/being will find the chest. If this occurs there is 10% likelihood that the chest will be ignored, 10% possibility that something will be added to the contents, 30% possibility that the contents will be exchanged for something else, 30% chance that something will be stolen from it, and 20% probability that it will be emptied.
Thus, a chance that the chest could be found even while the spell was running was part of the spell description itself in first edition.
What I would do
5e is a kinder, gentler playing experience than 1e was (I was there). Having players' chests found and taken while under an active spell, when that is not explicitly part of the 5e spell description, would be regarded as a 'jerk DM' move by most current players. Drawing on 1e lore and having this happen to NPCs in a 5e game, however, might be an effective a plot hook when one of them then hires the PCs to get their stuff back.
Should the players have this spell, a very effective villain could be made from an antagonist 'who has figured out how to find actively hidden chests' and is looting their contents. The players might have to thwart such a reprobate while taking extra precautions with their own things. Such a turn in the campaign would need to be clearly telegraphed first though, with the PCs hearing of this horror befalling other unlucky wizards long before it happened to them.