The shamrock plant is grown from a bulb, so, according to the Gardener's Rake, people sometimes think that it is dying when it really isn't. The good news is that you can care for your shamrock plant easily, and even if you believe it is dying, you can probably get it to come back.
Cut back your shamrock plant to allow it to rest. Most of the time, when a shamrock plant appears to be dying, it is actually just in need of an off-season, or a time in which it can rest. It grows from a bulb and is a perennial, so if it is dying at the end of a growing season, simply cut off the dying or dead portions and wait for the new growing season to start.
If you don't have a change in temperature coming, or your shamrock plant lives indoors, you want to cut back the plant as far as possible if it appears to be dying. Cut all of the dead or dying pieces off of it, and simply leave it be. Water the soil lightly after you have cut it back.
Care for your shamrock plant during its resting cycle. If it is outdoors and there is a winter or frozen season, pack some mulch or fertilizer around the part of the plant that you can see, to protect the main bulb.
If the plant is resting without a change in growing season, simply move it to the shade if possible. Continue to water lightly every week or so. Otherwise, let it be and wait for it to come back. As long as you keep the soil hydrated and keep it out of the bright sunlight, it will come back eventually.