Why do cooked potatoes taste bland when they cool down a bit?
I see multiple possible reasons for this. Here are some tests you can run. Be sure to run each test on a separate day, so you have a normal appetite for every test.
The first two tests are to determine if the change of temperature is actually the cause of the loss of flavor. The last two tests are to examine some other possible causes.
Test number one
Cook a potato as normal, put it on your plate and let it sit for 10 minutes, as though this is your second potato. Eat the cooled potato, and compare to how you remember your usual second potato tasting.

If the cooled potato seems just as bland/boring as the second potato normally is, you now know that temperature is a significant factor.
If you enjoy the cooled potato as much as you normally enjoy your first potato, you now know that the temperature is not what makes the difference.

Test number two
In this test, you eat two potatoes. The first potato is cool, and the second potato is hot. Start cooking a potato. After 20 minutes, start cooking another potato of the same size. When the first potato is cooked, take it out of the pot, put it on your plate, and let it cool for 10 minutes (just like in the first test). Eat the cooled potato. When you're done eating the cooled potato, the second potato should be finished cooking. Eat the second potato.

If you enjoy the second, hot potato more than you enjoy the first potato, you now know that temperature was the main issue.
The solution is to cook your two potatoes sequentially. Start cooking the second potato ten minutes after you start the first one. Eat each potato as soon as it's ready. That way you can eat both potatoes hot.
Or, use an insulating wrapper to keep the second potato warm while you eat the first potato. An oven mitt would probably work well for this purpose. However, as Kat suggested in the comments, it's possible that the second potato is actually getting over-cooked while it sits. If that's the problem, insulating the potato to keep it warm would make the problem worse. So you could do another test comparing the two methods (staggered cooking times vs same cooking time + insulating the second potato).

If you don't enjoy the second, hot potato as much as you enjoy the first, cold potato, you know that temperature is not the main issue. Proceed to the next few tests.


Test number three
I always find my mouth feels quite dry after eating a potato. Perhaps you're not drinking enough water with your meal.  After finishing your first potato, get a full glass of water. Drink the entire glass (at a reasonable speed, not gulping it). Let it settle. Then eat the second potato.
Test number four
Sometimes the tastebuds get tired of eating a single thing. One solution is to introduce a small amount of a strongly contrasting flavor. So, try eating a palate cleanser between the two potatoes. Since potato is a very mild taste, you will probably want a sharp flavor, either spicy, sour or bitter. Some options include: pickles, pickled ginger, a slice of apple, bitter herbs, a dab of horseradish sauce, sauerkraut, chutney, kimchi, a slice of lemon or lime (eat the fruit and the rind for a combination of sour and bitter).
The palate cleanser doesn't need to be major component of the meal, but rather a garnish of something that will startle, surprise or shock your tastebuds. After a bit of this surprising flavor, returning to the potato should seem safe and comforting. Like how a chilly breeze makes you enjoy snuggling into a warm sweater.

Potatoes are actually known to have a high satiety index compared to nutritionally similar foods like pasta and rice. That means they give you the &quot;physiological and psychological experience of fullness.&quot; Because of this, some people actually recommend potatoes as a food to help you eat less.
If none of the above tests helps you find a solution, it might be that your body is telling you not to eat the second potato. Perhaps it's telling you you've already had enough calories. Or, maybe you still need more calories, but your body wants them in a different form (such as green vegetables, protein and/or fat). It might be worth comparing your usual daily food intake to a recommended balanced diet, just to make sure you're actually getting the nutrition you need.