auto reset an Arduino using ftdi - DTR signal stays low and needs to go high after 1-50ms
This is the schematic of the Arduino pro mini and take a look at the reset mechanism:



There are two ways to reset the device: By holding down the reset push-botton/switch or by driving the line (DTR or RTS) low. 

Note: Some applications for arduino use DTR, others use RTS, but both seem to work. I used RTS and had no issues.

Now, back to the reset. When the DTR/RTS is pulled low, the capacitor, \$C_2\$, starts to charge up from zero to the \$V_{cc}\$ value. This is essentially asserting a reset, because the time it takes to reach logic one (maybe 0.7*Vcc), is enough for the micro to interpret it as a logic 0 (up to 0.3*Vcc). 

Also, usually the FTDI applications use pullup resistors connected to the DTR/RTS lines since these are open drain. Like this one:



The pullup is not mandatory in this case because the Pro Mini, has one on board on its reset pin, but it doesn't hurt either.

Like I said, DTR or RTS may work, I am speaking based on my personal experience with this but that's how I got it to work. Also, it seems like Arduino supports the use of either, just test it out and see what happens. 

I found all the images on the SparkFun website. The FTDI image is for the 'FTDI cable' which uses the RTS line. The 'FTDI breakout' board, as they call it on there, uses the DTR line instead and no pullups...

Arduino Pro Mini

FTDI Cable

FTDI Breakout board