Can a SEO Specialist guarantee constant position for a site in any search engine for a long time period?

Nope. Nope. Just Nope. No SEO expert can guarantee a constant position for a long time period. And Please! if anyone is promising you anything of the sort. . . RUN AWAY FROM THE PERSON. He is making false promises!

Thank you for inviting me.

No SEO expert can ever guarantee a constant position in the search result. the reason  being that

• the search algorithm changes frequently: so you can make educated guess and then it is all trial and error.
• There are over 1 billion websites and many new one are added each minute - this will affect your position.
• other Websites are optimizing for ranking constantly this will also affect your position.

(Anyone who says he/she can guarantee your position should be a fraud and may be using black hat tricks of SEO - the algorithm will soon catch-up with you and down your site)

No SEO expert can give guarantees search engine results. 

Never. It will be a fluke. They cannot control the search engines. Any SEO consultant who gives you guarantees is not a professional because, he/she cannot influence what search engine companies like Google, Bing, Yandex et al should be doing. They should only be able to guarantee best practice and leave the rest to search engines to decide