Short answer:
On most or all habitable moons of gas giant planets the typical nights should last several times as long as the eclipses caused by the shadows of the planets the habitable moons orbit. Thus you should ask what the effects of those long nights are likely to be, instead of the effects of the much shorter eclipses.
Long answer:
40 hours per month of the moon? And how long is the month of the Earth like moon?
An Earth like astronomical body, habitable for beings like humans, should be at least 3,000,000,000 years old, and possible billions of years older.
However, considering an Earth-mass exomoon around a Jupiter-like host planet, within a few million years at most the satellite should be tidally locked to the planet—rather than to the star
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/1
Thus the habitable moon's day should equal its monthly orbit around it's planet, while its year should its primary planet's orbit around their sun.
The synchronized rotation periods of putative Earth-mass exomoons around giant planets could be in the same range as the orbital periods of the Galilean moons around Jupiter (1.7–16.7 d) and as Titan's orbital period around Saturn (≈16 d) (NASA/JPL planetary satellite ephemerides)4.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/1
The longest possible length of a satellite's day compatible with Hill stability has been shown to be about Pp/9, Pp being the planet's orbital period about the star (Kipping, 2009a).
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/1
The planet's year as it orbits around the sun of their system should be at least nine times as long as the habitable moon's month and day as it orbits around the planet, and possibly several times nine times as long as a month/day.
If the habitable moon's month/day might be 1.7 to 16.7 Earth days, as suggested above, and the length of the year must be at least 9 times as long, the length of the year of the habitable moon should be at least about 15.3 to 150.3 Earth days.
Detected exoplanets considered to probably be within the habitable zones of their stars have days ranging in length from 6.1 Earth days to 384.8 days.
https://en.wikipedia.org/wiki/List_of_potentially_habitable_exoplanets1
We might arbitrarily assume that 2,000 Earth days is the longest possible year for a habitable world - Ceres, near the outer edge of the most optimistic habitable zone calculated for our sun has a year 1,683 Earth days or 4.60 Earth years long.
https://en.wikipedia.org/wiki/Ceres_(dwarf_planet)2
https://en.wikipedia.org/wiki/Circumstellar_habitable_zone#/media/File:Estimated_extent_of_the_Solar_Systems_habitable_zone.png3
And we might arbitrarily assume that 5.0 days is the minimum possible year for a habitable planet.
And thus the month/day of a habitable moon should be less than 0.5555 to 222.2222 Earth days in order to be less than one ninth the length of the planetary year.
An eclipse period of 40 Earth hours or 1.666 Earth days would require a month/day of considerable length.
The closer a moon orbits to its planet the more tidal heating will heat it. The closer a moon orbits to its planet the more sunlight reflected from its planet will heat it. Thus a moon orbiting too close to its planet will become too hot and suffer from runaway greenhouse heating and loss of its water into space.
Moons at distances between about 5 and 20 planetary radii from a giant planet can be habitable from an illumination and tidal heating point of view, but still the planetary magnetosphere would critically influence their habitability.
http://adsabs.harvard.edu/abs/2013arXiv1309.0811H4
The shadow cast by a planet upon its moon's orbit will have a diameter of 2 planetary radii. If the moon's roughly circular orbit has a radius of 5 to 20 planetary radii it will have a circumference of 31.4159 to 125.6636 planetary radii or 15.70795 to 62.8318 times the diameter of the shadow cast by the planet.
Thus the month/day of the habitable moon will be about 15.70795 to 62.8318 times as long as the period in eclipse - if the moon orbits the planet in the same plane, or close to it, as the planet orbits their sun. If the moon's orbital plane is more than slightly different from that of the planet, the moon will be eclipsed by the planet on rare occasions or will never be eclipsed by the planet.
If the habitable moon and its planet orbit in the same plane, the habitable moon's month/day should be about 15.70795 to 62.8318 times as long as the period in eclipse once per month/day.
If the of the planet orbited by the habitable moon should be at least nine times the length of the month/day of the habitable moon, there should be at least 9 eclipses during a year of the planet, and the year of the planet should be at least 141.37155 to 565.4862 times as long as an eclipse period.
If the eclipse period is about 40 Earth hours or 1.6666 Earth days as said in the original question, the habitable moon's month/day will be about 628.318 to 2,513.272 Earth hours, or 26.179916 to 104.7196 Earth Days. Thus the length of the planet's years should be about at least 235.61924 to 942.47694 Earth days or at least 0.6450 to 2.5803612 Earth years.
However, considering an Earth-mass exomoon around a Jupiter-like host planet, within a few million years at most the satellite should be tidally locked to the planet—rather than to the star
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3549631/1
Thus the month/day of the habitable moon should always be several times as long as the length of the period that habitable moon spends in the eclipse by its planet.
And if the calculation that a habitable moon's orbital distance should be five to twenty planetary radii is correct, the habitable moon's month/day should be about 15.70795 to 62.8318 times as long as the period in eclipse.
If the original question is hoping for an eclipse lasting longer than one day of the moon, the answer must be no, because a moon cannot have a day of arbitrary length. The length of a moon's day must equal the length of its month, since almost all moons will be tidally locked to keep one side always facing their planet and the other side always facing away from the planet.
There is some hope for a habitable moon to rotate faster than its orbital period around it planet.
Since the satellite's rotation period also depends on its orbital eccentricity around the planet and since the gravitational drag of further moons or a close host star could pump the satellite's eccentricity (Cassidy et al., 2009; Porter and Grundy, 2011), exomoons might rotate even faster than their orbital period.
The sources are:
Cassidy T.A. Mendez R. Arras P. Johnson R.E. Skrutskie M.F. Massive satellites of close-in gas giant exoplanets. Astrophys J. 2009;704:1341–1348.
http://iopscience.iop.org/article/10.1088/0004-637X/704/2/1341/meta5
Porter S.B. Grundy W.M. Post-capture evolution of potentially habitable exomoons. Astrophys J. 2011;736:L14.
http://iopscience.iop.org/article/10.1088/2041-8205/736/1/L14/meta6
But I have my doubts that the rotation period of a moon could ever be shorter that the time it spends in the shadow of its planet during an eclipse.
Thus on most or all habitable moons of gas giant planets the typical nights should last several times as long as the eclipses caused by the shadows of the planets the habitable moons orbit. Thus you should ask what the effects of those long nights are likely to be, instead of the effects of the much shorter eclipses.