I have lots of RC cars and have had Projects Lab programs for years with dozens of my own cars and hundreds of kids getting their own cars through me. I have had many Associated RC10Ts and Lost XXXTs, Traxxas and ECX AMPS. As kits have become more and more rare over the years for several years the AMP BTD kit was my fave. The weak point is what you are experiencing = the electronics are too low grade for the rest of the kit. I just got two Slash kits and now currently consider that the best option -- $200 at aMain.
With your ailing Amp I would get a FlySky FS-GT2B for $35
https://tinyurl.com/bdz6mnm4 OR
Flysky RC FS-GT3B on Amazon for $39 -- This has more screens/modes and may be more complicated for younger kids.
OR a Spectrum STX2 aMain $44
https://tinyurl.com/8hm8edn2
or on eBay $29 -- Then you'll have a radio with memory for several cars.
You'll also need an esc but the Amp is a very good car for kids once you have good electronics.
Hobbywing HWI30120201 Quicrun 1060 Brushed ESC (1/10) $22
https://tinyurl.com/56y8yxf4
If you also end up with a Slash (used ones aren't much cheaper but you can keep your eye out) But, again, the Slash kit or RTR for $200 at aMain is the deal. Electronics are sturdy and Traxxas is in USA and I've always received GREAT support = calling and getting through to a knowledgeable and caring person.
Ending up with two 1/10 trucks will be fun for you and your son or his friends. The Amp is a sturdy truck once you've upgraded the electronics -- so is the Slash with the stock electronics.
I agree with 95PGT =
make sure you centered your servo = could be the whole problem. If not, do not replace the Rx/ESC combo as they are cheap and frail (a poor choice by ECX for an otherwise great entry-level car)
Two cars may seem a bit pricey BUT if you get your kid involved in the driving, charging and repairing it will involve real life project based education above most sterile school academics.
I'll soon have classes for kids about learning Engineering through building the Slash on Outschool -- Watch for my "Overview of RC Cars" there in the next week or two -- The Building will come after that. If your son is young you can help him but the more he can do the better for him.
It will be annoying that the ECX and Traxxas have different connectors. You can sort out adaptors -- ask aMain for advice but I will also cover this dilemma in my Outschool classes over the summer.
Please keep us posted about your decisions.
Al Mayberry