Is profici the present passive infinitive of proficio?

I checked the conjugation of proficio online and it did not give the present passive infinitive.

It’s an intransitive verb and nobody ever used it, although in principle you could build one as you did.

This word is in the book I am using and it is giving me fits because I am having trouble translating this one sentence. I did find translations for proficio so I will go back and see if I can come up with a suitable translation.

Actually it could be present infinitive passive, since the verb can mean also to grow, to increase for inanimate objects:

B. Of inanim subjects, to grow, increase (mostly post-Aug.): “id (vitis genus) quod umore proficit,” Col. 3, 20: “proficiente pretio,” rising, Plin. 14, 4, 6, § 57.—In pass.: “sed etiam ad summam profectum aliquid puto,” Cic. Att. 7, 13, 1: “postquam nihil proficiebatur,” Plin. 6, 26, 30, § 122.

Please post the sentence.

Is profici the present passive infinitive of proficio?

With due respect to Bedwere, the answer is yes. This verb is not necessarily intransitive: it can mean something like “accomplish”. Lewis and Short give an example specifically of profici – Caesar Gallic Wars 3.21:

ubi diligentiā nostrorum nihil his rebus profici posse intellexerunt

“when they realized that nothing could be accomplished by these efforts [things] on account of the diligence of our men”

http://perseus.uchicago.edu/cgi-bin/philologic/getobject.pl?c.14:5346.lewisandshort

here is the sentence: ad reliqui temporis pacem atque otium parum profici

I will post my translation but it does not agree with with translations by others: that toward peace and leisure of the remaining time progressed too little;

Commentarii de bello Gallico
Liber VII

66
Interea, dum haec geruntur, hostium copiae ex Arvernis equitesque qui toti Galliae erant imperati conveniunt. Magno horum coacto numero, cum Caesar in Sequanos per extremos Lingonum fines iter faceret, quo facilius subsidium provinciae ferri posset, circiter milia passuum decem ab Romanis trinis castris Vercingetorix consedit convocatisque ad concilium praefectis equitum venisse tempus victoriae demonstrat. Fugere in provinciam Romanos Galliaque excedere. Id sibi ad praesentem obtinendam libertatem satis esse; > ad reliqui temporis pacem atque otium parum profici: > maioribus enim coactis copiis reversuros neque finem bellandi facturos. Proinde agmine impeditos adorirentur. Si pedites suis auxilium ferant atque in eo morentur, iter facere non posse; si, id quod magis futurum confidat, relictis impedimentis suae saluti consulant, et usu rerum necessariarum et dignitate spoliatum iri. Nam de equitibus hostium, quin nemo eorum progredi modo extra agmen audeat, et ipsos quidem non debere dubitare, et quo maiore faciant animo, copias se omnes pro castris habiturum et terrori hostibus futurum. Conclamant equites sanctissimo iureiurando confirmari oportere, ne tecto recipiatur, ne ad liberos, ne ad parentes, ad uxorem aditum habeat, qui non bis per agmen hostium perequitasset.

Caesar is relating the speech of Vercingetorix. In the context profici seems to be impersonal: there was little progress, they were not progressing much, or something like that.

I don’t think profici here is impersonal – it’s passive. The subject is parum, which can be used as a substantive/noun. “Little was being accomplished.” But your looser translation is perfectly correct, and in fact more idiomatic English: “there was little progress.”