as long as your REP(re-entry permit) is valid, you will not lose your PR status.
(A SPR will lose his/her SPR status if he/she leaves/remains outside Singapore without a valid REP)

for your case, what you have to do is to renew your REP, you can renew your REP at any Singapore Overseas Mission through your local representative or by post to Immigration & Checkpoints Authority.

P.S. All successful applicants must return to Singapore to collect their REPs.

and the documents needed to renew REP:

1. A letter (issued not more than one month ago) from the employer addressed to the Controller of Immigration, stating the date of employment, position held and monthly salary;
2. A statement from the CPF Board showing the CPF Contribution History for the last 12 months;
3. Income Tax Notices of Assessment for the last 3 years.

therefore

>>>PR要到期乐,能在国外renew 吗?本人现在不在新加坡, 短期内也回不来.是否可以在新加坡的当地大使馆办理哪
you can try to renew it while you are oversea, but you have to return to Singapore to collect your REP

>>>如果当时没有工作也可以renew嘛?
I dont think so