Had a quick read up, apparently there are indoor and outdoor bonsai, I'm assuming yours is indoor. Book says watering is by immersion (which is what you're doing now anyway) once a day or every couple of days, depending, or by watering can with a fine rose, compost should be kept damp, but not waterlogged, stand the plant on a pebble tray kept topped up with water to increase humidity around the plant, brightly lit spot out of direct sun, out of draughts and away from heat sources. Should be stood outside during summer months, brought back in as weather cools down. Rainwater recommended.
Seems to me you're not watering anywhere near enough by doing it once a week, that's the trouble I think.

Congratulations on owning your first bonsai. Here's a little help to get you started.
Watering needs: Rainwater is best however if you water with tap water allow it to stand for 24 hrs in an open topped container before use. This allows it to reach room temp. and facilitates chlorine escape from the tapwater. Water from the top as this will introduce air into the soil whilst flushing harmful salts out of the soil. Only immerse the pot in water if the soil has dried out too much and water will not penetrate the compost. Leave it immersed until no bubbles emerge from the pot/soil, lift out of water allow excess water to drain out and check watering needs daily. To do this stick a bbq skewer or a wooden chopstick deep into the soil, leave it for five minutes before pulling it out. If its wet - don't water. If its dry/nearly dry - water. When you water, gently dribble water all over the surface of the soil. Continue to do this until water runs from the bottom of the pot.

Fertilising needs: Feed every two to three weeks during the growing season with half strength plant food starting one month after the leaves have opened (as your tree is evergreen and in shock, stop feeding and wait for it to recover before commencing feeding).

Light requirements: Keep out of direct sunlight means its not recieving full sun ALL day. It needs some sun. Try an east/southeast facing window. Keep out of midday and hot afternoon sun. Stand the pot on a humidity tray to increase air moisture levels around the tree.Without a humidity tray its like trying to grow a tropical rainforest tree in the desert (air too dry). During warm summer weather (now!) place outside and only bring it indoors when the weather turns cool. This should benefit your tree.

Temperature requirements: Keep out of draughts and away from sources of heat (fire, radiator, TV, etc.). Fluctuating temperatures can cause problems with leaf loss, so take tree out of window during hours of darkness as the temp. can drop dramatically during the night. Check this out yourself by placing your hand near the window when its dark and feel how much cooler it is.
That should help for now. Remember - growing a bonsai is a learning curve, don't give up. I've yet to hear of a bonsai enthusiast who hasn't lost at least one bonsai at one time or another.
For more info. on chinese pepper bonsai go to
http://www.joebonsai.com/chinese-pepper-bonsai-care

or for a great bonsai forum site try
http://www.bonsaitreeforums.com

or try
http://www.bonsai4me.com

I hope this helps. If it doesn't at least it gave you something to read. ;-))

Wow, comprehensive advice! Many thanks.
I'll go and sit it on the patio for a day or two to get some light and fresh air (and rain), take things from there.
I'd hate it to die.....