A lot of the time if the corp has a server that you simply can’t get into, it’s a good idea to turn your attention to other servers. If you simply can’t get into the remote, but it looks like he’s setting up to score out of it, maybe try pressuring HQ in the hopes of stealing the agendas he’s hoping to score or hitting R&D and finding his agendas before he does. After all, the remote does nothing if they can’t put anything in it.
Also, just drawing like crazy for answers is a good idea as well. Don’t be afraid to discard things that aren’t helpful right now. Even discarding programs that you think you might need later is a fine thing with Shaper, since Clone Chips will bring them out the moment you need them. You might not want to discard them until you have a clone chip, but once you do it can be just fine.
Some games are also unwinable if you get a completely terrible draw and your opponent gets precisely what they need. But these are usually few and far between with PPVP Kate, and a lot of time it comes down to trying to analyze where the game got away from you. A lot of times it can look like one thing, but in fact be another. As an example, I lost a game (winner’s bracket semi-final in an SC) where I was playing Butcher Shop (an NBN kill deck that uses Midseasons to bury the runner in tags and then kill them with Traffic Accident and Scorch) to a MaxX deck. There was a point where he hit an agenda, turning on Midseason’s, but I didn’t have enough money to both tag him and kill him. I wanted to land enough tags where he wouldn’t just pay down the trace and then try and slowly clear tags over the next couple turns before I could assemble the money to kill him, so I hit him with enough to land 5 on him even if he payed max on the trace, spending myself down to 2 credits in order to do so, thinking my next turn would be credit, Traffic, Scorch. His turn he runs R&D and I opt to not rez the Wraparound, figuring it probably wasn’t an agenda, but it was, putting him on 5 points. He runs again, and this time I have to rez the Wraparound or otherwise risk losing the game to a topdeck. He finishes his turn and I spend mine clicking for credits to kill him next turn. He discards Corroder with his MaxX ability and clone chips it out on a run on R&D, finding the agenda on top.
For a long time, I was kicking myself for not just being safe and rezzing that Wraparound the first time on R&D. I could have clicked for credits and killed him the next turn. I played the game over in my head for days after that, really regretting that choice. However, after a while, I realized that my real problem was that I just over-Midseasons’d him. I didn’t need to bump the trace that much at all in order to assure that he had 2 tags on him next turn since there was nothing he could do from 0 credits to remove even 2 tags. If I had saved 2 credits on the trace, I’d have had the 2 to safely rez Wraparound and kill him the next turn, since all he could do was remove a single tag, still leaving him at 2.
So basically, really try and analyze what went bad where. Sometimes it can be trashing a SanSan in R&D, setting yourself too behind in money to come back reasonably. Sometimes it can be not running simply to make the corp rez ICE so they don’t have enough money to rez the ICE they need to to score, or to simply have enough money to advance agendas. As I said, sometimes there’s actually nothing you can do, but it’s rare.
Hopefully this didn’t get too long-winded somewhere in there. Glad you’re enjoying the game =)