If you added together the time spent in every shower you have ever taken, it would likely add up to a little more than a full year of your life. That's a lot of showering. Since you spend a lot of time getting clean, the area where you do your personal cleaning should also stay clean. If you are seeing an orange stain beginning to appear on your shower mat, know that several issues can cause the discoloration, and taking action is important to prevent further staining or serious health issues.
Bacteria
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The most likely culprit behind your stained shower mat is a bacteria called Serratia marcescens. This bacteria is fairly common in the environment and is not harmful but is tough to get rid of. Serratia loves moisture and will thrive in areas where there is a lot of standing water or where moisture can be easily trapped (like under a mat.) If you suspect that bacteria is the cause, bleach the mat with a 50/50 mixture of bleach and water. If the mat is fabric, you can run it through the washing machine; but if it is vinyl, plastic or another synthetic source, you will need to apply the liquid bleach (preferably with a spray bottle) and rinse after 5 to 10 minutes. In either case, dry the mat thoroughly after bleaching, and try to keep it as dry as possible.
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Copper in Water
If the orange stain is closer to red in color, you may have a problem with copper in your water. Although the source of the stain will probably never go away, treating copper stains is relatively easy. Apply a mineral stain cleanser (such as CLR, or a comparable product), and follow the directions to remove the stain. Depending on the concentration of copper in your water, you may need to repeat this process anywhere from once a week to monthly. Though the copper stain is not harmful, it is quite unsightly and can ruin your mat if you aren't careful.
What Not to Do
If you see an orange stain on your bathmat, there are several things you definitely should not do under any circumstances. Most importantly, do not soak your bathmat; no matter the cause or severity of the stain, soaking the mat in water will only exacerbate the issue, and you'll likely damage your mat beyond repair. Another important thing not to do is to relocate the mat. Moving it to a new area will only spread the orange stain and, if you have grouted tile or vinyl flooring, they could also be stained by the mat.
When to Throw the Mat Away
Unfortunately, if you let the orange stain build up too much, your mat may not be salvageable. If you see that the edges of your mat are eroding, the orange stain is spreading (even after cleaning) or the color of the stain has changed, you should throw the mat away and immediately sterilize the area where the mat was before buying a replacement. All of these signs can indicate strong bacterial colonies or extreme mineral corrosion, both of which cannot be stopped with simple cleaning.