A road bike tire outfitted with an inner tube will leak enough that it will require topping up at least weekly up to 2x/wk in my experience. Eighty to 100 psi is a lot for a tube to hang on to. If your tire is going completely flat over the duration of days or a week, this is definitely caused by a hole in the tube, a crack in the stem or the valve within the stem is either loose or damaged.
When one encounters a completely flat tire containing a butyl rubber tube (most common, non-latex) that was fully inflated days, weeks or even a month or more prior, one needs to evaluate the tube and stem for competency. This is best done outside the rim for a few reasons other than thoroughness.
I would first remove the the rim from the bike and then the tire containing the tube from the rim. Best practice would be to keep everything oriented the same so when the leak in the tube is found, you can go back and examine carefully that area of the tire and rim for possible causes. This is one reason why mechanics orient the label on the right side of the tire with the valve hole in the rim. For the odd nondirectional tire, you'll need to keep track of which is the right side when it was mounted.
With the tire off the rim, I'll strip the tube from it. The side of the tube mounted toward the right side of the bike I'll try and keep facing up or to my right. I'll put enough air in the tube to make it fairly rigid. At this point it will typically be larger than the tire that contains it. I feel it's best, especially when faced with a slow leak, to fully submerge the tire and look for air bubbles. I've used buckets or a rectangular plastic container that's 6 inches or so deep and dip one section of tube at a time. Pinhole leaks will be evident right away. I've had some that were slow enough that it took several seconds for an air bubble to form on the tube surface and then release. So be patient with each section. Note that several small air bubbles will form on the surface of the tube from the act of submersion. You can wipe these away under water.
It's almost a certainty that the leak you describe will show itself with the submersion method by a column of bubbles rising from the site. There may be more than one, so keep going until 100% of the tube is checked including the valve stem. You're most likely to have a Presta valve for a wheel fitted to a Trek Domane. After the tube is inflated prior to it's bath, screw down the valve to seal it. This way a non-sealing valve stem can be caught.
Holes that are found should be marked. I use a gold colored sharpie to circle them. You may also mark them by putting the end of a toothpick in it. Encountering two holes side by side--the so called, "snakebite," is an indication of a pinch flat. These happen when an under inflated tire encounters an obstacle and deforms enough that the tube is pinched between rim and the deformed tire. Make sure your tires are adequately inflated prior to a ride.
Note,too, where on the tube the hole was found. It's important to note whether the hole(s) are located on the inner or outer perimeter of the tube, and then go back to the corresponding area of tire or rim to look for possible causes. Check that the rim tape is covering the spoke nipples and that the end of the spokes aren't protruding through the nipples too far. On the tire side, it's rare but not unheard of to find the hole maker still in the tire. So search for any foreign objects in the tire. I use this opportunity to wipe out the inside of the tire with a damp cloth.
Finally many people like the ease and no-mess of patches that you simply peel and stick over the hole. The best fix (imo), is using the rubber vulcanizing* cement with an appropriate, sticky-backed patch. I use some sort of pressure (like a soft clamp or book) on the repair area for several minutes after to ensure a good patch that won't roll up at the edges. Otherwise follow the directions of the product.
*I'm using a loose definition of vulcanizing here, but technically correct. The rubber cement has a solvent that will soften the roughened area of the tube to be patched. This then helps the patch and tube molecules to bond as one.