I have experience with this. I have an '03 cobra convertible and if it ain't raining the roof is down. Around here (Portland, OR) that makes for a lot of up / down on the ol' soft top!
Ok, most likely where your leak is coming from is the bottom corner(s) of the back window insert section of the convertible top. This section can be patched temporarily with some success, but you will eventually need to replace that section - which is separate from the top section, so no need to replace the whole top.
To find your leak, put your roof about half way up / down. Now lift the folds / flaps along side the window. Look closely down in the lower corners where the top meets the sides ~ you will probably see cracks / splits where the canvas top transitions to the under-layer (seems to be a heavy duty vinylized / plasticised canvas). Cracks / splits are bad and will spread and let water in. You will need to seal these up, which is a temporary measure. You may also notice that there is a piece of plastic "support" or reinforcement that is kinda sharp and pokey on the ends and rubs on the top as it is lowered. This can wear holes as well.
From inside the car, if you look behind the headliner at the back window you will see a sort of fold in the top that runs down the sides of the back window. Feel along there and you will probably find a frayed spot or two, or small hole, which is where the water dribbles in. Check THOROUGHLY for multiple holes behind those side sail panels (mine had multiple holes on each side) and seal all those up.
Another way to find the inside holes is to hose down the back window and then look for where the water is dripping in from.
In the past I used Tear Aid (Type A, clear) to patch the holes and it worked well. It is a rubber sticker patch for repairing camping gear that you can cut to size. I patched inside and out. Be sure to clean the area good with alcohol before applying the patches. This stops the water coming in for a while ~ depending on how often you cycle the top. I'm finding that after the summer season of many top up / down cycles, the patches need replaced by the Fall / rainy season. So I was re-patching every fall for 3 or 4 years before the splits got so bad that I couldn't completely seal them anymore.
You may try a fabric eppoxy instead / in addition to the Tear Aid, since the outside holes can be difficult to cover with a patch because they are so close to the back window seams. I never did try the fabric epoxy though.
The good thing is that the holes are hidden from view, so you can use anything you want in order to get the job done :-)