Bullpup designs are mechanically more complex, requiring a long trigger linkage, and control system linkages. This seriously degrades both control feel, and reliability, and increases bulk and weight (there may be engineering solutions to this problem).
If current munitions infrastructure and laws allowed for electronic trigger, feed, and ignition systems, this would be a non issue, and the bullpups advantage may outweigh it's several disadvantages; but for now, that's not an option (also, electronic systems have their own issues).
If a bullpup has a catastrophic failure, instead of the explosion being six or eight inches in front of your eyes, it's right at your eyesocket, or touching your cheekbone or ear. The only good thing is, if the bolt flys back, it doesn't end up in your eye socket.
Most bullpups also eject hot brass, and vent hot gasses in the vicinity of your eyes and ears (some eject downward or forward, which is a better solution for a bullpup, if it's engineered properly).
Mag changes on most bullpups are slower (sometimes much slower) because they require more repositioning, that positioning can be awkward, and can be difficult to see (if necessary) without fully dismounting the rifle.
A conventional rifle allows you to see your mag changes, and is more easily maneuvered with your dominant hand, which makes mag changes easier in general.
More importantly a human being can naturally bring their hands together in the dark. As a basic design guideline, magwells should either be in your dominant hand, or just in front of it; because it is far more difficult to manipulate anything dexterously that is located behind your dominant hand.
Because of the positioning of the magazine (usually the part of a gun extending lowest) close to your shoulder when the weapon is mounted, bullpups can be difficult to fire while prone (though this is common with some other rifle designs as well).
Note in the pictures below, the magazine is by far the lowest point of the rifle; and being located behind the dominant hand and close to your shoulder; when you drop prone it will tend to strike the ground forcing the muzzle downward.
This can also cause problems with mags being warped, ripped out of the magwell, having the baseplate broken off, or the rifle itself being ripped out of the users hand when hitting the deck.
A conventional rifle with a long magazine can have issues with dropping prone as well, but because the mag is positioned forward of the dominant hand, instead of forcing the muzzle down, it will tend to force the muzzle up; and though it's not advisable to use the magazine as a monopod, it's possible. With a bullpup, it isn't.
This isn't an issue for rifles that are generally fired off bipods, so in an SAW or LMG role, the bullpup may be an appropriate solution (though having the feed system in such tight quarters with your shoulder and cheek is its own issue).
Charging the rifle and manipulating the operating handle is often more difficult, and sometimes can't be done without dismounting the rifle, or reaching over the rifle with your support hand (again, some conventional rifles do share this weakness; and this is a problem that can easily be solved with proper engineering).
Most bullpups can only be operated from the right shoulder; or if switchable, can only be operated from one shoulder without being reconfigured (this is changing, with the adoption of forward ejection mechanisms).know of, can be fired from the left shoulder.
Because of the way most bullpups eject their brass, and cycle their actions; attempting to operate the weapon from the wrong shoulder will result in hot brass being ejected directly into your face, and possibly injuring the user... or they my simply not be able to cycle at all.
Bullpups are naturally balanced in a non-instinctive way.
This is really the biggest problem, and the one that is hardest to solve with engineering.
The balance point on most bullpups is in between your hand and your shoulder when mounted, which is unnatural. We have a natural tendency to try to balance things between our hands, not between our hand and shoulder.
The only way to correct this is to put heavy things in front of your dominant hand, or to make the weapon short and light enough that this won't make a difference (and even then it will still be more awkward and less instinctive to point; but several modern bullpups have taken the second approach).
This balance will tend to make a bullpup tend to shift its butt under recoil, unless it is very tightly mounted to your shoulder; particularly during rapid fire. This tendency is somewhat countered by the position of your support hand so far forward on the barrel, by the fact that the overall leverage moment of the muzzle is lower (the muzzle isn't as far from either your shoulder, or your dominant hand), and by the fact that most bullpups have straightline recoil.
A conventional rifle is balanced in between your dominant and support hands, and there are good reasons for that. A human being naturally handles things that balance in the palm, or in front of your dominant hand, better, because we naturally want to balance things between our hands.
Under recoil, the muzzle of a conventional rifle rises, but just from gravity will fall into you support hand again without actually holding or pulling it down, because the fulcrum of the lever is in your dominant hand, and the balance point is in front of the fulcrum.
http://anarchangel.blogspot.ae/2005/03/why-bullpups-are-persistently-bad-idea.html?m=1