There is no time-limit
The rules for concentration are simple, they take a Standard action to use. Be that concentrate on a spell effect to keep it going, or concentrating on a spell with a long cast time. We know we have spells with an hour long cast times (see Occult Rituals), and spells with no limit on how long you can concentrate on their effects(see Audiovisual Hallucination and Wall of Fire).
None of those spells and mechanics actually penalize the caster for doing that all day. As such, I don't see a reason to penalize a caster for using Detect Magic all the time either. This is no different from moving stealthly for hours, or wearing heavy armor while traveling. It just takes a little extra effort on their mind, which can easily be interrupted by external sources (such as rain or combat).
However, keep in mind that all spells have visual effects, even those without components. As such, mundane characters (and those without ranks in Spellcraft) might consider this offensive and/or scary, and react negatively against the character. Merchants may think that they are trying to fool them in some way, and guards may think they are up to something.
Concentration and Perception
Concentrating on a spell will not fully take your attention away, as Perceiving something is usually a passive reaction, while focusing your attention on something is simply a Move action, as has been clarified how Stealth vs Perception works in Ultimate Intrigue (pg. 187), describing how active (like search for traps or hidden doors) and automatic perception (notice something sneaking behind you) works:
There are two ways Perception checks happen in the game. The first way is automatic and reactive. Certain stimuli automatically call for a Perception check, such as a creature using Stealth (which calls for an opposed Perception check), or the sounds of combat or talking in the distance. The flip side is when a player actively calls for a Perception check because her PC is intentionally searching for something. This always takes at least a move action, but often takes significantly longer.
The Core Rulebook doesn’t specify what area a PC can actively search, but for a given Perception check it should be no larger than a 10-foot-by-10-foot area, and often a smaller space if that area is cluttered. For instance, in an intrigue-based game, it is fairly common to look through afiling cabinet full of files. Though the cabinet itself might fill only a 5-foot-by-5-foot area, the number of files present could cause a search to take a particularly long time.