1) Shoot more rounds through the gun first...I always shoot 200 rounds of BALL through any gun before it goes into service (and even then I shoot 50 rounds of the intended carry ammo). Every so often you see a gun that doesn't benefit from a break-in, but that is the exception rather than the rule.
2) You did lube it up before you started firing it, right?
3) If the situation continues, last round failure to fire is in general a magazine issue or a weak grip (anticipating the end of the string, the shooter loosens his/her grip, which will stall a lightweight pocket pistol).
4) "Everybody is having trouble with LCPs..." Really? Considering I've shot more rounds through more different LCPs than anyone else in the country who DOESN'T work at the Ruger factory, it's news to me. And to the people I talk to on a regular basis, who are some of the top instructors in the country.
And let me reiterate my basic mantra...while forums — including this one — are entertaining and interesting, they often do not provide a truly useful, or even fair, view of a gun. Here at DOWN RANGE we try to point you in a direction, but you are going to have to go there yourself.
I have discovered about a million ways to make a gun malfunction...nothing to do with the gun part of the system, but a failure on the human part of the system...which is nonetheless a part of the system. In any gun failure, the first thing I try to do is eliminate my own actions as a contributing factor to the stoppage. Then I try to make the gun repeat the stoppage (and, generally, if it won't repeat the stoppage, it means I may have discovered a million and one ways to jam a gun!).
If it is a repeating failure — the last round never chambers — and it is a new gun, I send it back and ask that it be made right. Every single manufacturer will make it right, because they need customers to stay in business. If the factory gunsmith can't make the error repeat in the shop — and believe me, it does happen...a lot — then I will step them through how the gun failed for me, including ammo, weather/environmental conditions (hot/cold; wet/dry; blowing dust/no wind), status of the gun (clean/dirty; just lubed/lubed once in 1984; brand new/owned a month; whatever); my own experience as a shooter; any anomalies I noticed prior to or during the gun's failure (Did the gun's recoil feel the same or different? Did the gun's noise seem different? Was there anything at all different about how the gun felt when it jammed?); how did the gun respond to basic remedial actions (disassembly-clean-relube-reshoot, the equivalent of rebooting a stalled computer)...
...I have gone through this process on some enormously complicated gun problems...a 9mm Kimber that I considered melting into a paperweight; a custom Colt/Caspian racegun that flatly refused to race; the Commander From Hell; but eventually we debugged the guns (These were not new guns! If I have a problem with a new gun, just like you guys I send it back...that's why God made warranties).
The problem with racing to the Internet and announcing you have a "5% failure rate" is that by tomorrow morning the forums will be baying that everybody knows "LCPs are suffering a 5% failure rate," which is not true. What is true is that one gun had 2 failures, both different in nature, in 40 rounds, and in the absence of additional information, we can only speculate what caused the stoppages.
I suppose in an ideal world, all guns would be 100% 100% of the time...unfortunately, machines are made by humans, and humans make mistakes.
Michael B