This depends on a lot of things.
The idea of preheating is that you want to get all the surfaces inside your oven (walls, floor, door, racks) up to the desired cooking temperature. This makes for more even temperatures throughout the oven, and gives a little thermal mass so you don't lose ALL your heat when you open the door for a few seconds or put something cold in there.
Then there's the question of what you're putting in the oven. An aluminum sheet with a few room temperature cookies on it won't pull the temperature in the oven down like a 25 pound turkey that's 40F/5C inside. You want to be more careful to do a complete preheat if you're going to be soaking up a lot of your starting heat.
Our oven, which has a large baking stone in the bottom all the time, takes a while to get uniformly up to temperature, even after the oven says it's preheated, because the stone doesn't heat up as fast as the rest of the surfaces. It takes at least 20 minutes after the "I'm fully heated" beep before the stone is fully up to temp. We have problems with things baking poorly if we don't preheat for quite a while, but on the upside, if we put a cold roast in or open the door a lot, the temperature in the oven stays pretty high.
If your oven is lightweight, flimsy or drafty, it may be as hot as it's going to get the moment the preheat alert goes off.
45 minutes is probably a lot more preheat than you'll need in almost any case. In some cases even 15 minutes is more than you need. It really depends on your oven and what you're putting in.
Cooking temperature and time are determined by a number of factors. The idea is to get the inside of the product properly cooked before the outside dries out, becomes tough, or becomes unpleasantly dark or even burned. At the same time, you usually want the product to get nicely browned (adds flavor and looks nice) before the inside is overcooked. So it's a balance.
Factors which influence appropriate temperature and time include:
ingredients: High protein ingredients (like meat or eggs) easily become tough when overcooked. High sugar or starch recipes will tend to brown or burn more easily.
moisture level: For some products, such as popovers or many kinds of pastry, steam is an important leavening agent, and a high temperature is called for. In other products, like cookies, one of the goals of baking is to drive off excess moisture. And in still others, moisture is absorbed into the other ingredients.
shape: A fat, round loaf will usually need a longer cooking time and lower temperature than a thin, flat pizza or a long, skinny baguette because it takes longer for the center of the loaf to heat up.
pH: Changing the pH of the product will change how it browns.
leavening: Some chemical leavening, like double-acting baking powder, activates at a certain temperature.
personal preference: At the end of the day, the most important factor is whether you like the way the product turned out. If you like a crispier crust, change the temperature and/or cooking time to suit your taste.
Any baking recipe should specify the temperature and cooking time, unless perhaps it's from a book that specifies those things for a number of recipes at once. If not, find a similar recipe and use the temperature specified there, but keep a close eye on the product during the baking process. Learn how to tell when the product is done. For cakes, you usually go by color for the outside, and by temperature or using a toothpick or wooden skewer for the inside. (Briefly: poke a wooden toothpick into the center of a cake; if it comes out with wet batter, keep cooking; if it comes out clean and dry, it's probably overcooked; if it comes out with a few crumbs stuck to it, it's probably perfect.)
Best Answer
After opening the door the temperature is supposed to drop a few degrees since it's exchanging heat with the outside air (which is usually colder than in the oven...).
The cake batter should also absorb part of the heat put out by the oven, by heat transfer. So if your oven is very small (like an oven-toaster-grill), weak, leaking large amounts of heat (through openings or cracks) or you're putting a huge amount of really cold cake batter the temperature might not rise back to previous levels.
So I'd say it's not normal - at least I never saw such a large temperature drop for such a long time. Trying bake a smaller cake, or checking that the baked goods are not blocking the heating element or the air circulation inside the oven.
Try also putting your thermometer in a different position inside the oven and see what's the difference - maybe just part of the oven is not getting up to temp, since you said your cakes are baking fine.