Also:
It's absolutely true that most engineering/science/math courses end up moving through content too quickly to give students a grasp of conceptual understanding or appreciation of the application of the processes being studied (in the standard formulation of content) to processes in the natural world or in the design of technological innovations. If you look at the required curriculum, professors usually have to move at least one chapter per week. It takes skill and experience to learn how to navigate that without reducing the course to rote... both on the part of the professor and the student.
So here's my advice:
1) Talk personally to upper-level students at your university (in your degree program or related degrees, and students that you know and respect... perhaps honors students) to discover which professors might be the best to take. I generally looked for the professors that were considered difficult but worth the added effort because they were excellent.
2) On your own end, read the material and start to work through examples and problems in the text before class sessions. This will allow you to have some familiarity with the material so that you can listen for the interesting things the professor says in class... and ask questions about the material (either in class or afterwards, during office hours etc.). Note that for every class it's generally the case that you should be putting in 2-3 hours of study per week for every credit hour of class (so that being a full-time student with 12- 18 hours of credits should be a full time job, if not more!)... often you should really be putting in MORE than 2-3, if you're really working (school was at least a 60-80 hour week for me at times!)
Even so, sometimes it takes years to really gain insight into concepts and really understand them, and if you want to get though a degree program in a given amount of time, you sometimes just have to (sadly) slog though.

Appreciation and understanding should develop more and more over time, and this development should never stop, as long as you maintain your curiosity. What I'm concerned about now is that you do state you are losing your curiousity. So, my advice on this front is that you should try:
3) To sometimes look at simple texts: like introductory concept texts or materials (ex. Bloomfield's "How Everything Works" etc.) and demonstration guides (like Mr. Wizard's things or The Exploratorium notebook). You can find cool demos to try online, and some science museums have good websites. Sometimes the most interesting things can have the math removed... and you can think about how to model the math (ex: ask yourself: Why do race cars have spoilers, and then how would I calculate the force generated by the spoiler... what variables would I need to know?).
4) To build something complex. I've been most recently fascinated by online guides to building cheap vacuum pumps (although I haven't done it yet due to time!). I've known students and colleagues that have built tesla coils, robots that track their paths and avoids objects by sensing, etc. Building provides a LOT of conceptual understanding, as you have to design and surmount hurdles!
5) To do outreach or tutoring. This actually makes TEACHING fun (getting to find new resources for my class and generating new problems for students)... perhaps it might help you keep your curiosity if you do some outreach to students at lower levels. A professor at our university in the department of education surprisingly has a great link to engineering here and gets students to volunteer tutor at local high risk schools. I didn't do this as a undergrad, but I was on the tutoring staff at our university for science and math (covering all chemistry, physics and math topics)... it often made me develop better understanding as I had to review and work through concepts that I hadn't experience for a while... asking the tutored students to first explain what they were thinking to me, then working through possible misconceptions! Oh yeah -- you can also dabble in tutoring online here!
