Twice a day (after rising and before sleeping) I pray a mystery of the Rosary. I tend to finish the Rosary, and then say aloud my intentions, which consist of spiritual things (salvation of the world, obtaining virtues, for souls in Purgatory + those who have led me to the Faith) and also temporal things (just simple petitions for studies, work and such). This prayer routine has went on for about five months approximately. 

Recently I've been having trouble saying my intentions aloud after finishing the Rosary. The recitation of the Rosary itself is not of any concern, minus the usual distractions due to human defects. But after finishing it, I struggle to articulate aloud my intentions, as in I feel like I can't bring myself to say it. However interiorly I'm able to recollect some of those intentions. 

Is this a cause for concern and any advice is welcome! 

Make your intentions before starting the Rosary and they count for the whole Rosary regardless of when you complete it, whether you pray five or fewer decades, all 15 decades, it doesn’t matter. When done for the day, remind Our Lady by saying something like, “and the all the intentions attached.” No need to repeat them. If you’ve forgotten them, Mary hasn’t!  Truthfully, I’ve never heard of leaving ones intentions to the very end, especially if your life’s duties result in having to pray the Rosary in bits and pieces.

Another suggestion if you have time and the wherewithal, and you have many intentions, write down a list. Divide them into groups of five or 15. Keep the strips of paper with your Rosary or maybe use plastic or something you can write on and erase. Literally attach each reminder to the Rosary. As you come to each decade, make your smaller number(s) of intention(s) before each decades and include that person/item(s) in your meditation upon that particular decade. When done, erase or leave the intentions as desired. This method focused your prayers in a more specific manner. 

I other way is acceptable and easier. If you remember someone left out, ask Our Lady to attach the forgotten intention and She will. 

I hope this helps.

I highly suggest this little book, "Secrets of the Rosary".  It will relax you. Mary knows your hearts intentions. When Mary took Christ Jesus for the Presentation Simeon said, many thoughts of men would be laid bare?  Mary knows.  

If you did read this book, I found it necessary for me to read sections again. 

Sounds as if you have a very good petition that the devil doesn't want you to have, thereby making it difficult for you to articulate it.  Tell him to go to hell.  Realize why it's difficult and you'll persevere.

As for when to mention your intentions, remember they are actually petitions or requests for something so always after you have performed some act of adoration or homage or reverence... e.g. the Mass, rosary, stations, litany, chaplet, etc etc.  then you actually. with humility. have something to offer, whereas if you mention your request first ....well it's about what you want rather than paying homage.
We were always taught when practicing our devotions to give or render before you request.
Don't go empty handed.

Thank you, yes, that's what I thought so as well. But other commentors seems to think that mentioning intentions should come before instead.