As has mentioned, this situation will not work. In fact, there is no stable configuration which would give every point on a planet perpetual "daylight."
You could say that in the hypothetical case of a system with a whole bunch of stars, it would be possible to have at least one star in the planet's sky at any given time.
However, multiple star systems are associated with a number called "Hierarchy" as shown here.
http://en.wikipedia.org/wiki/Multiple_starFor a system to be stable, the ratio of the distances of consecutive levels in the mobile diagram must be fairly high; about 5:1 (this is the minimum ratio, aka periapsis distance of more distant body to apsis distance of closer body). Planets also take up a spot in the mobile diagram; planets trying to share orbits with stars will be captured or ejected.
A distant binary or multiple illuminates a planet in pretty much the same way a single star would.
Finally, if a star is too far away, the light it produces can't really be considered "daylight."
http://en.wikipedia.org/wiki/Daylight. 1 lux is on the order of magnitude of the full moon, so it's a decent cutoff. This corresponds to a distance of about 500 AU for a sunlike star, and less for K and M class stars.
Basically, this means that even in the best case scenario of a planet orbiting an M-class star in a hierarchy 4 (not counting the planet) system, there will only be 5 stars (or groups of stars) capable of illuminating a planet.
In such an extreme case, parts of a planet could experience periods of hundreds of years where at least one star was always visible (akin to Isaac Asimov's "Nightall") but overall the amount of daylight a planet got would depend on the seasons (very complicated seasons).