The German Federal Office for Migration and Refugees gives the following information, which will answer your question partially:
"Asylum proceedings can be discontinued. This takes place if
the asylum application is withdrawn. [...] Once the asylum proceedings have been finally completed, a renewed asylum application may be filed. This "follow-up" application claims that there has been a change to the factual or legal situation once the non-appealable decision has been handed down (see Initial, Second and Follow-up applications)." (Source: http://tinyurl.com/yaz9w2rt
But to answer your question completely, we have to consider the Dublin-III-Regulation. For details see this information provided by the European Commission for Migration and Home Affairs: http://tinyurl.com/y7wg7jkq
In Germany the Federal Administrative Court made a judgement that a delined procedure for granting the right of asylum may not lead to an automatic refusal if you apply for asylum in Germany at a later date (Source: http://tinyurl.com/ydgv3uq8
- German language).
Time issues seem to play a subordinate role, I didn't find any limiting regulation. This may be due to the fact that the human rights situation is not really predictable in every country.
If you need some help, you may try e.g. Jesuit Refugee Service: http://tinyurl.com/ycxftfyn