10 kHz bandwidth at 10 MHz is very tight for a R-L-C filter. Even if you could put a high enough order filter together, it would be useless due to part tolerance errors.
The only passive way to do this that has any chance of working is to use a 10 MHz crystal. You should still preceed it with a L-C filter to eliminate frequencies that can make the crystal resonate at overtones (harmonics). The L-C pre-filter will also help reduce the power of the signals the crystal has to get rid of.
There is another way, but it is definitely active and more complex, and uses the technique of hetrodyning. The basic concept is to shift the original frequency to a lower value where the desired bandwidth is a much larger fraction of the frequency, then shift the result back. The relatively wider bandwidth at the lower frequency makes a filter more tractable. Old AM radios used this technique, but didn't bother shifting back since they only wanted the amplitude and could get that from the shifted frequency.
450 kHz was a common IF (intermediated frequency) for AM radios intended to receive the commercial AM band from about 550 kHz to 1.7 MHz. The tuning knob would adjust the local oscillator, which needed to be 450 kHz less than the reception frequency. The result would go thru a 450 kHz narrow band filter and amplifier. This needed about 20 kHz bandwidth, which is 4.4% of 450 kHz. That was doable with a few carefully factory-tuned parts. In "super hetrodyne" radios, the tuning knob also adjusted a L-C filter to roughly select the RF frequency of interest. Note that due to how product modulation works (which is how the local oscillator was "mixed" with the filtered RF), there are actually two RF frequencies that result in the 450 kHz IF. These are the local oscillator plus 450 kHz (the desired RF frequency), and the local oscillator minus 450 kHz, called the "image" frequency. The original L-C filter on the RF needed to be tight enough to eliminate the image frequency before the hetrodyning.
You should also consider what you want to do with the final narrow band signal. If you just want to AM detect it, for example, then there may be other ways than starting with a very narrow band filter. It's not worth going into this without more information about what exactly you are trying to do, where this 10 MHz signal is coming from, what kind of modulation you want to detect, how much out of band noise the input signal contains, etc.
One ting that jumps out is you have not selected a model for the diode - right click and select one from the list. Otherwise it may not simulate correctly.
I think what you are seeing may be to do with the rectifier not being able to sink current (only a small amount will flow through the 200k resistor), so the input signal will not look as it would unloaded, it will "charge" to it's peak. Then the larger the cap, the longer the fall time when the signal stops. Try putting a non-inverting buffer in between the rectifier and Sallen Key input. This should make both filters respond in the same way.
Best Answer
In order for electrolytic capacitors to perform correctly, they need to be forward-biased. You cannot reverse-bias them and have them perform properly.
Even though your input signal has a DC component, your feedback capacitor is still going to spend some of its time with its polarity reversed as the op-amp attempts to follow the filtered input signal, which means the feedback capacitor won't perform as a capacitor. Instead, it will function as a capacitor half of the time, and an ever-hotter short-circuit the other half of the time. It won't blow up as quickly as if you attached it in reverse to, say, a 12V power supply, but it won't last very long, and your circuit won't perform as expected. What will probably happen is that your voltage regulator feeding the op-amp will get very hot and burn out before the capacitor boils. So, you cannot use an electrolytic for the feedback capacitor.
An electrolytic may work for your capacitor connecting the positive differential input to ground, assuming your input signal is centered at some DC component. But, if you modify this circuit and remove the DC component of the input signal, and feed the op-amp with two supply rails, one positive and one negative, then you can't use an electrolytic capacitor in either position.
It's probably safest just to go with non-polar capacitors, rather than mix-and-match.