There was an interesting conversation at the RTCUK Sleepover about DEET maybe degrading climbing ropes. It was scary enough to make you think twice about risking Lyme's or a nasty fall. After all, as a solvent DEET will melt plastic and denature your sunglasses, camera and so on.
I couldn't find anything definitive online, but everything you can find points to this quote from a report which now seems to be unavailable:
“Summary of Nylon, PET and Spectra Chemical Resistance to DEET
Many climbers have in the past worried about the effects of accidentally spilling bug repellent on their climbing ropes. The following is the result of preliminary testing of deet and other bug repellent chemicals.
Samples of nylon, polyester, and spectra were submitted for chemical resistance testing for DEET (N,dimethyl-m-toluamide). The three samples were immersed separately in “CUTTER” and “OFF” brand insect repellent for a period of twenty-four hours at room temperature. “OFF” contains 95% Deet (N-dimethyl-m-toluamide) while “CUTTER” contains only 7% Deet and probably some oil based solvents as well. The results of the testing indicate no loss of strength as measured by tensile strength retention in any of the three samples.
There was one interesting anomaly that occurred only in the case of Nylon and the “CUTTER” brand insect repellent. As mentioned before there was no loss of strength for any of the samples but here there was a 25% increase in the elongation and a decrease in modulus. This basically means that a rope made entirely or mostly out of Nylon may become “rubbery” with a significant amount of exposure to “CUTTER” or other insect repellents with large amounts of oil based solvents.
However, with regard to the chemical in question, DEET, there appears to be no effect on any of the physical properties of the three samples. Hence as “CUTTER” contains only 7% DEET the change in the Nylon elongation and modulus must come from the other solvents in the product. It is suggested that if a rope has significant amounts of Nylon to use insect repellents with 95-100% Deet instead of ones with some Deet and large amounts of other oil based solvents.
Please keep a major factor in mind in regards to this study/testing. The only two brands tested were OFF and Cutter and were specific formulas of those brands. So we can’t necessarily say that all bug repellent products with DEET will not harm the stated materials. Other brands and other formulas could contain a substance other than what was in the two formulas tested. In other words, it is probably safe to say DEET itself has no effect but there can be other chemicals in other repellents that may.”
Personally, I'm taking this as permission to not worry. The most up-to-date forum discussion about this I could find was this one, and there seem to be no accounts online of rope failure after DEET contact. Your mileage may vary, but for me avoiding the relative certainty of again having to extract gangs of voracious parasites from my nethers beats the theoretical risk of equipment failure.