Partial indulgences can always be sought after, any number of times a day. It's pretty much the same thing as doing atonement for your sins (or offering up your sufferings for those in Purgatory).
3 ... Tradition also teaches, however, that an indulgence can be attached to various works of private or public devotion. Therefore such works of charity and repentance which ought to be given greater emphasis in our times can be enriched with an indulgence. But all such works endowed with indulgences should never in any way be set aside or apart from the Mass and the sacraments. The Mass and the sacraments remain the outstanding sources of sanctification and purification - no matter how good any such indulgenced works and patiently endured sufferings may be. Such good works and sufferings become the faithful's offering which is joined to Christ's offering in the Eucharistic Sacrifice ...
- Norms, Handbook of Indulgences.
There are three main ways to obtain partial indulgences.
I. A partial indulgence is granted to the Christian faithful who, while performing their duties and enduring the difficulties of life, raise their minds in humble trust to God and make, at least mentally, some pious invocation.
II. A partial indulgence is granted to the Christian faithful who, prmpted by a spirit of faith, devote themselves or their goods in compassionate service to their brothers and sisters in need.
III. A partial indulgence is granted to the Christian faithful who, in a spirit of penitence, voluntarily abstain from something which is licit for and pleasing to them.
The Church is intent especially upon expressing the three principal ways, longstanding in its practice, which make it possible to fulfill the divine command to repent. These are prayer, fasting, and works of charity - even though fast and abstinence have a had a privileged place. These ways of penance have been shared by all the centuries ...
- Grants, Handbook of Indulgences.
Also, if any of the requirements for a plenary indulgence are lacking, the indulgence is partial.
26. To acquire a plenary indulgence it is necessary to perform the work to which the indulgence is attached and to fulfill the following three conditions: Sacramental Confession, Eucharistic Communion, and prayer for the intention of the Sovereign Pontiff. It is further required that all attachment to sin, even venial sin, be absent.
If the latter disposition is in any way less than perfect or if the prescribed three conditions are not fulfilled, the indulgence will be partial only.
- Norms, Handbook of Indulgences
As always these should be seen in light of our own repentance and in doing penance for the faithful departed souls in Purgatory (a spiritual work of mercy). Our Lord calls us to "repent! For the Kingdom of God is at hand." And these offerings are signs of our repentance.
I guess a partial indulgence is what our parents often told us when we would whine or when we had a minor injury and they would tell us "offer it up!"
My main goal in this is for people to pray for and help the souls in Purgatory. If you can help get them to Heaven by your prayers and sacrifices, they will assuredly help you with their prayers as well.