Yep, it is a browser limitation on the event frequency. The feeling was that 4 times a second is more than enough to update a time display in seconds and any faster is just wasting power. 4Hz is 2 times the Nyquist frequency for 1 second (1Hz) used for digital sampling. (So you're lucky it's not 500ms / 2Hz as that is all that is required.)
While I have never needed to do this, you can get a more accurate figure by accessing the HTML5 media element directly. jPlayer reads the media element info each time the timeupdate event occurs and puts it on the jPlayer status.
$("#My_Player").data("jPlayer").htmlElement.audio.currentTime
jPlayer uses an audio and a video element, so tweak that line as appropriate.
Since jPlayer might be using the Flash fallback, you need to check the HTML5 solution is being used.
$("#My_Player").data("jPlayer").html.used
I'm not sure how often the currentTime is updated on the media element, but it seems to change independent of timeupdate events.