How much Wi-Fi signal strength do I lose per foot of antenna cable?
Solution 1:
There is no arbitrary limit. Any increase in cable length will reduce signal strength. (So will the connectors that you'll need to connect another length of cable to this one.) As Burgi and DavidPosthill said in the comments, how much it's reduced for a given length depends on the cable and the frequency.
A common relatively inexpensive cable for short runs of WiFi antennas is LMR100. At 2.4 GHz (the common WiFi band), 15 feet of LMR100 will result in signal loss of about 6 dB. That's equivalent to dropping power to just 25% of what it was. (Each 3 dB = 50% gain or loss in power)
With LMR400 cable, your loss would be only about 1 dB! (But that cable is more expensive, and also a lot less flexible = more difficult to install.)
The loss in dB is linear with the cable length. So if you use 30 feet of LMR100 cable, your loss will be 12 dB (i.e. your signal is now about 1/16 the power that it was). With 7.5 feet, loss will be only 3 dB (you lose half of your signal).
All of the above numbers are for the 2.4 GHz WiFi band. For 5 Ghz it will be much worse.
Don't even think about using RG59 (the older, thinner coax that used to be used for TV cable and antennas and commonly is seen with "F" or BNC connectors attached; it's not even the right impedance) or RG58 (the right impedance, but still very lossy at these frequencies). These cable types aren't rated at all for use above 1 GHz.
You can find data sheets (with signal loss graphs) and calculators for various types of microwave coax all over the web. Here's a calculator (found at a cable dealer) that covers a wide variety of table types.
And to convert dB to ratios (or back), try this (Note, since this is signal loss we're talking about, enter the dB number as a negative number before pressing "calculate". Note also that you want the power ratio, not voltage.)
One last tip: Don't try to assemble cables yourself. Buy cables with the right connectors already attached. Very minor-seeming mistakes with connector assembly can cause huge losses at these frequencies. And absolutely do not cut the connectors off and try to splice the coax. Might as well throw the antenna away at that point.
Solution 2:
The short answer is:
Ideally you would have no cable. Every bit degrades the signal.
You get about 10 metres of cable before you need some kind of amplifier/booster/repeater, otherwise your signals about as good as dead.
Solution 3:
When you're trying to get actual practical information about the product, first step is to take a look at the product datasheet. So on TP-LINK's downloads website for linked product, you'll be able to download the datasheet. One you do, you'll be able ti find the exact cable type used there. In this case, it's RG-174.
Unfortunately, they did not specify exact manufacturer of the cable, so we need to go and look for some generic answers. Usually, losses are specified either per meter or per 100 feet and are frequency dependent, so let's see if we can try that for this cable.
Go to Google, type RG-174 coaxial cable losses 2.4 GHz. One of the results is this handy table. Looking there, you can find that RG-174 has around 1.7 dB attenuation per 1 meter, giving around 2.2 dB loss for the 1.3 m piece that comes with the antenna. Do keep in mind that the numbers are not for the specific cable you have, but for category, so don't be surprised if you find slightly different values elsewhere.