Light from an object and the intervening sky always add to make the object brighter than the sky. In the middle of a sunny day any DSO fuzzies up there will be just a tiny smidgen brighter than the adjacent sky.
As pointed out, the crucial factor is by how much brighter the [object+sky] resultant is than sky alone. And this limit varies by sky brightness and object contrast against this sky. Under a bright city sky an extended source can have surface brightness (SB) around 3.5 magnitudes fainter than the sky. But under a dark country sky *and* when using a small exit pupil, the object might require to be as bright as the sky, if not brighter, just to be detected. Visual system noise worsens as scene brightness decreases, thus rendering subtler contrasts ever harder to discern.
On top of this is the worsening visual resolving power with decreasing scene brightness. Whereas at photopic (daytime) brightness levels we can resolve on the retina down to 1-2 arcminutes, at the lower limit of brightness/contrast, where visual system noise is very much dominating, visual resolution has degraded to as poor as several *degrees*!
This therefore requires quite different minimum apparent angular size for detection as sky brightness and object contrast against the sky vary.
This can lead to interesting effects. For instance, consider a face-on spiral galaxy possessing a small, bright core in a very extensive, dim disk. Let's suppose the sky darkness would permit the disk system to be seen if sufficiently enlarged. The brighter core, in spite of its much smaller size, can be seen via not-so-large apertures because its higher surface brightness does not so adversely impair visual resolving power. The dimmer disk, however, demands that it subtend a larger minimum apparent size in order to be detected. And so until sufficient aperture/magnification is brought to bear, the small core is seen while, seemingly paradoxically, the much bigger disk remains quite invisible.
Obtaining a decent feel for how the matrix of factors sky SB, object SB, object size and varying visual resolving power work in concert to control object visibility can seem daunting. But with some time spent in study these contributing variables can begin to assemble into a coherent picture. The RASC's Observer's Handbook has a section dealing with this. And I've posted on the matter here at CN, producing a couple of charts by which to facilitate understanding. One such chart resides in my Gallery, linked to below, in my signature (if you've not disabled the display of sigs.)
My more recent chart appears in the following thread, in the Deep Sky Forum:
http://www.cloudynig...sibility-chart/
Edited by GlennLeDrew, 31 January 2017 - 03:17 AM.