Looking for a love story between an immortal and a mortal, can be any kind of immortal as long as he/she has lived for a very long time already and will continue so for eternity, the setting I want is that the mortal one (can either be the male or female lead) keeps chasing after the immortal who keeps refusing to fall in love afraid of the eternity of suffering after the other's death. I'd also like if in the end it indeed shows the immortal grieving after being alone for several years after the lover's death, but this isn't absolutely necessary...

Please, no yaoi, yuri, shounen-ai or shoujo-ai

thanks in advance

Kindan no Koi de Ikou.

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If I’m upset, hold me and tell me how beautiful I am.
If I growl, retreat to a safe distance and throw chocolate.

Not sure if it fits 100%, but you could try:
Immortal Rain
Kamisama Kiss

Hana to Akuma,

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"In a world where most people would be crazy, then it would be normal to be crazy and crazy to be normal... but then again, if you were normal, then you would be crazy... isn't it crazy what a paradox a little craziness can create?"

Thanks for the suggestions, but unfortunatelly I've already read or am reading all of them, great mangas all of them.
If anyone know more like those I'd be very grateful

not sure but maybe Blade of the immortal

masca
I second immortal rain
somewhat hanatsukihime
that's all I remember

Spice & Wolf (Novel)!! Well, I haven't gone that far into the story, but you can sense how it's going to end...

Sarashi Asobi mostly fits..